RS Aggarwal Solutions: Triangles | Mathematics (Maths) Class 6 PDF Download

 Page 1


( ) EXERCISE 16 A
Q.1. Take three non-collinear points A, B
and C on a page of your notebook.
Join AB, BC and CA. What figure do
you get ?
Name :
(i) the side opposite to C
(ii) the angle opposite to the side BC
(iii) the vertex opposite to the side CA
(iv) the side opposite to the vertex B
A
C B
Sol. A, B and C are three non-collinear
points in a plane. AB, BC and CA are
joined.
A
C B
(i) The side opposite C is AB
(ii) The angle opposite to the side BC is
A
(iii) The vertex opposite to the side CA is
B
(iv) The side opposite to the vertex B is
CA
Q.2. The measures of two angles of a
triangle are 72º and 58º. Find the
measure of the third angle.
Sol. The measures of two angles of a
triangle are 72º and 58º
But measure of three angles of a
triangle is 180º
Third angle will be = 180 – (72º + 58º)
= 180º – 130º = 50º
Q. 3. The angles of a triangle are in the ratio 1
: 3 : 5. Find the measure of each one of
the angles.
Sol. Sum of three angles of a triangle = 180º
Ratio of three angles = 1 : 3 : 5
 First angle 
180 1
1 3 5
180 1
9
20
º º
º
Second angle 
180 3
9
60
º
º
Third angle 
180 5
9
100
º
º
Hence, three angles are 20º, 60º and 100º
Ans.
Q. 4. One of the acute angles of a right triangle
is 50º. Find the other acute angle.
Sol. Sum of three angles of a right triangle
= 180º
 Sum of two acute angles = 180º – 90º
    = 90º
 Measure of one angle = 50º
 Second acute angle = 90º – 50º = 40º
Ans.
Q. 5. One of the angles of a triangle is 110º
and the other two angles are equal. What
is the measure of each of these equal
angles ?
Sol. Let the measure of each of the equal
angles be xº. Then,
xº + xº + 110º = 180º
(Angle sum property of a triangle)
2xº + 110º = 180º
2xº = 180º – 110º = 70º
Page 2


( ) EXERCISE 16 A
Q.1. Take three non-collinear points A, B
and C on a page of your notebook.
Join AB, BC and CA. What figure do
you get ?
Name :
(i) the side opposite to C
(ii) the angle opposite to the side BC
(iii) the vertex opposite to the side CA
(iv) the side opposite to the vertex B
A
C B
Sol. A, B and C are three non-collinear
points in a plane. AB, BC and CA are
joined.
A
C B
(i) The side opposite C is AB
(ii) The angle opposite to the side BC is
A
(iii) The vertex opposite to the side CA is
B
(iv) The side opposite to the vertex B is
CA
Q.2. The measures of two angles of a
triangle are 72º and 58º. Find the
measure of the third angle.
Sol. The measures of two angles of a
triangle are 72º and 58º
But measure of three angles of a
triangle is 180º
Third angle will be = 180 – (72º + 58º)
= 180º – 130º = 50º
Q. 3. The angles of a triangle are in the ratio 1
: 3 : 5. Find the measure of each one of
the angles.
Sol. Sum of three angles of a triangle = 180º
Ratio of three angles = 1 : 3 : 5
 First angle 
180 1
1 3 5
180 1
9
20
º º
º
Second angle 
180 3
9
60
º
º
Third angle 
180 5
9
100
º
º
Hence, three angles are 20º, 60º and 100º
Ans.
Q. 4. One of the acute angles of a right triangle
is 50º. Find the other acute angle.
Sol. Sum of three angles of a right triangle
= 180º
 Sum of two acute angles = 180º – 90º
    = 90º
 Measure of one angle = 50º
 Second acute angle = 90º – 50º = 40º
Ans.
Q. 5. One of the angles of a triangle is 110º
and the other two angles are equal. What
is the measure of each of these equal
angles ?
Sol. Let the measure of each of the equal
angles be xº. Then,
xº + xº + 110º = 180º
(Angle sum property of a triangle)
2xº + 110º = 180º
2xº = 180º – 110º = 70º
xº
º
º
F
H
G
I
K
J
70
2
35 .
 The measure of each of the equal
angles is 35º.
Q. 6. If one angle of a triangle is equal to the
sum of the other two, show that the
triangle is a right triangle.
Sol. Let the three angles of a triangle be A,
B, C. Then, A = B + C
Adding A to both sides, we get
A + A = A + B + C
2 A = 180º
(Angle sum property of a triangle)
F
H
G
I
K
J A
180º
2
90º .
 One of the angles of the triangle is a
right angle.
Hence, the triangle is a right triangle.
Q. 7. In a ABC, if 3 A = 4 B = 6 C,
calculate the angles.
Sol. In a ABC,
.
.
.
 3 A = 4 B = 6 C = 1  (say)
A =
1
3
B =
1
4
C =
1
6
 Ratio 
1
3
1
4
1
6
: :
 
4 3 2
12
: :
(LCM of 3, 4, 6 = 12)
= 4 : 3 : 2
Sum of angles ABC = 180º
 A =
180º 4
4 + 3 + 2
180 4
9
80
º
º
     B =
180º 3
9
60º
     
C =
180º 2
9
40º
Hence, angles of ABC are 80º, 60º and 40º.   Ans.
Q. 8. Look at the figure given below. State
for each triangle whether it is acute, right
or obtuse.
Sol. (i) It is obtuse triangle.
(ii) It is acute triangle.
(iii) It is right triangle.
(iv) It is obtuse triangle.
Q. 9. In the given figure some triangles have
been given. State for each triangle
whether it is scalene, isosceles or
equilateral.
C B
130°
A
60°
60° 60°
E F
D
Q R
P
90°
92°
Y Z
X
Page 3


( ) EXERCISE 16 A
Q.1. Take three non-collinear points A, B
and C on a page of your notebook.
Join AB, BC and CA. What figure do
you get ?
Name :
(i) the side opposite to C
(ii) the angle opposite to the side BC
(iii) the vertex opposite to the side CA
(iv) the side opposite to the vertex B
A
C B
Sol. A, B and C are three non-collinear
points in a plane. AB, BC and CA are
joined.
A
C B
(i) The side opposite C is AB
(ii) The angle opposite to the side BC is
A
(iii) The vertex opposite to the side CA is
B
(iv) The side opposite to the vertex B is
CA
Q.2. The measures of two angles of a
triangle are 72º and 58º. Find the
measure of the third angle.
Sol. The measures of two angles of a
triangle are 72º and 58º
But measure of three angles of a
triangle is 180º
Third angle will be = 180 – (72º + 58º)
= 180º – 130º = 50º
Q. 3. The angles of a triangle are in the ratio 1
: 3 : 5. Find the measure of each one of
the angles.
Sol. Sum of three angles of a triangle = 180º
Ratio of three angles = 1 : 3 : 5
 First angle 
180 1
1 3 5
180 1
9
20
º º
º
Second angle 
180 3
9
60
º
º
Third angle 
180 5
9
100
º
º
Hence, three angles are 20º, 60º and 100º
Ans.
Q. 4. One of the acute angles of a right triangle
is 50º. Find the other acute angle.
Sol. Sum of three angles of a right triangle
= 180º
 Sum of two acute angles = 180º – 90º
    = 90º
 Measure of one angle = 50º
 Second acute angle = 90º – 50º = 40º
Ans.
Q. 5. One of the angles of a triangle is 110º
and the other two angles are equal. What
is the measure of each of these equal
angles ?
Sol. Let the measure of each of the equal
angles be xº. Then,
xº + xº + 110º = 180º
(Angle sum property of a triangle)
2xº + 110º = 180º
2xº = 180º – 110º = 70º
xº
º
º
F
H
G
I
K
J
70
2
35 .
 The measure of each of the equal
angles is 35º.
Q. 6. If one angle of a triangle is equal to the
sum of the other two, show that the
triangle is a right triangle.
Sol. Let the three angles of a triangle be A,
B, C. Then, A = B + C
Adding A to both sides, we get
A + A = A + B + C
2 A = 180º
(Angle sum property of a triangle)
F
H
G
I
K
J A
180º
2
90º .
 One of the angles of the triangle is a
right angle.
Hence, the triangle is a right triangle.
Q. 7. In a ABC, if 3 A = 4 B = 6 C,
calculate the angles.
Sol. In a ABC,
.
.
.
 3 A = 4 B = 6 C = 1  (say)
A =
1
3
B =
1
4
C =
1
6
 Ratio 
1
3
1
4
1
6
: :
 
4 3 2
12
: :
(LCM of 3, 4, 6 = 12)
= 4 : 3 : 2
Sum of angles ABC = 180º
 A =
180º 4
4 + 3 + 2
180 4
9
80
º
º
     B =
180º 3
9
60º
     
C =
180º 2
9
40º
Hence, angles of ABC are 80º, 60º and 40º.   Ans.
Q. 8. Look at the figure given below. State
for each triangle whether it is acute, right
or obtuse.
Sol. (i) It is obtuse triangle.
(ii) It is acute triangle.
(iii) It is right triangle.
(iv) It is obtuse triangle.
Q. 9. In the given figure some triangles have
been given. State for each triangle
whether it is scalene, isosceles or
equilateral.
C B
130°
A
60°
60° 60°
E F
D
Q R
P
90°
92°
Y Z
X
Sol. (i) It is an isosceles triangle as it has
two equal sides.
(ii) It is an isosceles triangle as it has two
equal sides.
(iii) It is a scalene triangle as its sides are
different in length.
(iv) It is an equilateral triangle as its all sides
are equal.
(v) It is an equilateral triangles as its angles
are equal, so its sides will also be equal.
(vi) It is an isosceles triangle as its two base
angles are equal, so its two sides are equal.
(vii) It is a scalene triangle as its angles are
different, so its sides will also be different
or unequal.
Q.10. Draw a ABC. Take a point D on
BC. Join AD
How many triangles do you get ? Name
them.
C B
A
D
Sol. In ABC, D is a point on BC and AD
is joined
Now we get triangles ABC, ABD
and ADC
Q. 11. Can a triangle have :
(i) Two right angles
(ii) Two obtuse angles
(iii) Two acute angles
(iv) Each angles more than 60º
(v) Each angles less than 60º
(vi) Each angles equal to 60º
Sol. (i) No (ii) No    (iii) Yes
(iv) No            (v) No    (vi) Yes.
Q. 12. Fill in the blanks :
(i) A triangle has ............ sides, ............
angles and ............ vertices.
(ii) The sum of the angles of a triangle
is............ .
(iii) The sides of a scalene triangle are of
............ lengths.
(iv) Each angle of an equilateral triangle
measures............ .
(v) The angles opposite to equal sides of an
isosceles triangle are............ .
(vi) The sum of the lengths of the sides of a
triangle is called its............ .
Sol. (i) three, three, three.
(ii) 180º       (iii) different        (iv) 60º
(v) equal       (vi) perimeter.
( ) EXERCISE 16 B
Objective questions
Mark ( ) against the correct answer
in each of following.
Q. 1. How many parts does a triangle have ?
(a) 2 (b) 3
(c) 6 (d) 9
Sol. (c) 
.
.
.
 It has three sides and three angles
i.e. six.
Q. 2. With the angles given below, in which
case the construction of triangle is
possible?
L
Page 4


( ) EXERCISE 16 A
Q.1. Take three non-collinear points A, B
and C on a page of your notebook.
Join AB, BC and CA. What figure do
you get ?
Name :
(i) the side opposite to C
(ii) the angle opposite to the side BC
(iii) the vertex opposite to the side CA
(iv) the side opposite to the vertex B
A
C B
Sol. A, B and C are three non-collinear
points in a plane. AB, BC and CA are
joined.
A
C B
(i) The side opposite C is AB
(ii) The angle opposite to the side BC is
A
(iii) The vertex opposite to the side CA is
B
(iv) The side opposite to the vertex B is
CA
Q.2. The measures of two angles of a
triangle are 72º and 58º. Find the
measure of the third angle.
Sol. The measures of two angles of a
triangle are 72º and 58º
But measure of three angles of a
triangle is 180º
Third angle will be = 180 – (72º + 58º)
= 180º – 130º = 50º
Q. 3. The angles of a triangle are in the ratio 1
: 3 : 5. Find the measure of each one of
the angles.
Sol. Sum of three angles of a triangle = 180º
Ratio of three angles = 1 : 3 : 5
 First angle 
180 1
1 3 5
180 1
9
20
º º
º
Second angle 
180 3
9
60
º
º
Third angle 
180 5
9
100
º
º
Hence, three angles are 20º, 60º and 100º
Ans.
Q. 4. One of the acute angles of a right triangle
is 50º. Find the other acute angle.
Sol. Sum of three angles of a right triangle
= 180º
 Sum of two acute angles = 180º – 90º
    = 90º
 Measure of one angle = 50º
 Second acute angle = 90º – 50º = 40º
Ans.
Q. 5. One of the angles of a triangle is 110º
and the other two angles are equal. What
is the measure of each of these equal
angles ?
Sol. Let the measure of each of the equal
angles be xº. Then,
xº + xº + 110º = 180º
(Angle sum property of a triangle)
2xº + 110º = 180º
2xº = 180º – 110º = 70º
xº
º
º
F
H
G
I
K
J
70
2
35 .
 The measure of each of the equal
angles is 35º.
Q. 6. If one angle of a triangle is equal to the
sum of the other two, show that the
triangle is a right triangle.
Sol. Let the three angles of a triangle be A,
B, C. Then, A = B + C
Adding A to both sides, we get
A + A = A + B + C
2 A = 180º
(Angle sum property of a triangle)
F
H
G
I
K
J A
180º
2
90º .
 One of the angles of the triangle is a
right angle.
Hence, the triangle is a right triangle.
Q. 7. In a ABC, if 3 A = 4 B = 6 C,
calculate the angles.
Sol. In a ABC,
.
.
.
 3 A = 4 B = 6 C = 1  (say)
A =
1
3
B =
1
4
C =
1
6
 Ratio 
1
3
1
4
1
6
: :
 
4 3 2
12
: :
(LCM of 3, 4, 6 = 12)
= 4 : 3 : 2
Sum of angles ABC = 180º
 A =
180º 4
4 + 3 + 2
180 4
9
80
º
º
     B =
180º 3
9
60º
     
C =
180º 2
9
40º
Hence, angles of ABC are 80º, 60º and 40º.   Ans.
Q. 8. Look at the figure given below. State
for each triangle whether it is acute, right
or obtuse.
Sol. (i) It is obtuse triangle.
(ii) It is acute triangle.
(iii) It is right triangle.
(iv) It is obtuse triangle.
Q. 9. In the given figure some triangles have
been given. State for each triangle
whether it is scalene, isosceles or
equilateral.
C B
130°
A
60°
60° 60°
E F
D
Q R
P
90°
92°
Y Z
X
Sol. (i) It is an isosceles triangle as it has
two equal sides.
(ii) It is an isosceles triangle as it has two
equal sides.
(iii) It is a scalene triangle as its sides are
different in length.
(iv) It is an equilateral triangle as its all sides
are equal.
(v) It is an equilateral triangles as its angles
are equal, so its sides will also be equal.
(vi) It is an isosceles triangle as its two base
angles are equal, so its two sides are equal.
(vii) It is a scalene triangle as its angles are
different, so its sides will also be different
or unequal.
Q.10. Draw a ABC. Take a point D on
BC. Join AD
How many triangles do you get ? Name
them.
C B
A
D
Sol. In ABC, D is a point on BC and AD
is joined
Now we get triangles ABC, ABD
and ADC
Q. 11. Can a triangle have :
(i) Two right angles
(ii) Two obtuse angles
(iii) Two acute angles
(iv) Each angles more than 60º
(v) Each angles less than 60º
(vi) Each angles equal to 60º
Sol. (i) No (ii) No    (iii) Yes
(iv) No            (v) No    (vi) Yes.
Q. 12. Fill in the blanks :
(i) A triangle has ............ sides, ............
angles and ............ vertices.
(ii) The sum of the angles of a triangle
is............ .
(iii) The sides of a scalene triangle are of
............ lengths.
(iv) Each angle of an equilateral triangle
measures............ .
(v) The angles opposite to equal sides of an
isosceles triangle are............ .
(vi) The sum of the lengths of the sides of a
triangle is called its............ .
Sol. (i) three, three, three.
(ii) 180º       (iii) different        (iv) 60º
(v) equal       (vi) perimeter.
( ) EXERCISE 16 B
Objective questions
Mark ( ) against the correct answer
in each of following.
Q. 1. How many parts does a triangle have ?
(a) 2 (b) 3
(c) 6 (d) 9
Sol. (c) 
.
.
.
 It has three sides and three angles
i.e. six.
Q. 2. With the angles given below, in which
case the construction of triangle is
possible?
L (a) 30º, 60º, 70º (b) 50º, 70º, 60º
(c) 40º, 80º, 65º (d) 72º, 28º, 90º
Sol. (b) 
.
.
.
 Sum of three angles of a triangle is
180º.
Q. 3. The angles of a triangle are in the ratio
2 : 3 : 4. The largest angle is
(a) 60º (b) 80º
(c) 76º (d) 84º
Sol. (b) 
.
.
.
 Largest angle
180 4
2 3 4
180 4
9
80
º º
º
.
Q. 4. The two angles of a triangle are
complementary. The third angle is
(a) 60º (b) 45º
(c) 36º (d) 90º
Sol. (d) 
.
.
.
 A triangle has 180º and if two
angles are complementary i.e. sum of
two angles is 90º, then third angle will be
180º – 90º = 90º.
Q. 5. One of the base angles of an isosceles
triangle is 70º The vertical angle is
(a) 60º (b) 80º
(c) 40º (d) 35º
Sol. (c) 
.
.
.
 Sum of three angles is 180º and
sum of two equal angles = 70º + 70º =
140º, then third angle will be 180º – 140º
= 40º.
Q. 6. A triangle having sides of different lengths
is called
(a) an isosceles triangle
(b) an equilateral triangle
(c) a scalene triangle
(d) a right triangle
Sol. (c) 
.
.
.
 A scalene triangle has different
sides.
Q.7. In an isosceles ABC, the bisectors of
B and C meet at a point O. If A
= 40º, then BOC = ?
(a) 110º (b) 70º
(c) 130º (d) 150º
Sol. In an isosceles ABC, B = C
and bisector of B and C meet at O
and A = 40º
O
A
40º
B C
B = C = 
2
º 40 º 180
= 
2
º 140
 = 70º
2
1
B = 
2
1
C = 
2
º 70
 = 35º
Now in OBC
BOC + OBC + OCB = 180º
BOC + 
2
1
B + 
2
1
C = 180º
BOC + 35º + 35º = 180º
BOC = 180º – 70º = 110º (a)
Q.8. The side of a triangle are in the ratio
3 : 2 : 5 and its perimeter is 30 cm. The
length of the longest side is
(a) 20 cm (b) 15 cm
(c) 10 cm (d) 12 cm
Sol. Side of a trianlge are in the ratio 3 : 2 : 5
and perimter = 30 m
Length of longest side = 
5 2 3
5 30
= 
10
5 30
 cm = 15 cm (b)
Q.9. Two angles of a trianlge measure 30º and
Page 5


( ) EXERCISE 16 A
Q.1. Take three non-collinear points A, B
and C on a page of your notebook.
Join AB, BC and CA. What figure do
you get ?
Name :
(i) the side opposite to C
(ii) the angle opposite to the side BC
(iii) the vertex opposite to the side CA
(iv) the side opposite to the vertex B
A
C B
Sol. A, B and C are three non-collinear
points in a plane. AB, BC and CA are
joined.
A
C B
(i) The side opposite C is AB
(ii) The angle opposite to the side BC is
A
(iii) The vertex opposite to the side CA is
B
(iv) The side opposite to the vertex B is
CA
Q.2. The measures of two angles of a
triangle are 72º and 58º. Find the
measure of the third angle.
Sol. The measures of two angles of a
triangle are 72º and 58º
But measure of three angles of a
triangle is 180º
Third angle will be = 180 – (72º + 58º)
= 180º – 130º = 50º
Q. 3. The angles of a triangle are in the ratio 1
: 3 : 5. Find the measure of each one of
the angles.
Sol. Sum of three angles of a triangle = 180º
Ratio of three angles = 1 : 3 : 5
 First angle 
180 1
1 3 5
180 1
9
20
º º
º
Second angle 
180 3
9
60
º
º
Third angle 
180 5
9
100
º
º
Hence, three angles are 20º, 60º and 100º
Ans.
Q. 4. One of the acute angles of a right triangle
is 50º. Find the other acute angle.
Sol. Sum of three angles of a right triangle
= 180º
 Sum of two acute angles = 180º – 90º
    = 90º
 Measure of one angle = 50º
 Second acute angle = 90º – 50º = 40º
Ans.
Q. 5. One of the angles of a triangle is 110º
and the other two angles are equal. What
is the measure of each of these equal
angles ?
Sol. Let the measure of each of the equal
angles be xº. Then,
xº + xº + 110º = 180º
(Angle sum property of a triangle)
2xº + 110º = 180º
2xº = 180º – 110º = 70º
xº
º
º
F
H
G
I
K
J
70
2
35 .
 The measure of each of the equal
angles is 35º.
Q. 6. If one angle of a triangle is equal to the
sum of the other two, show that the
triangle is a right triangle.
Sol. Let the three angles of a triangle be A,
B, C. Then, A = B + C
Adding A to both sides, we get
A + A = A + B + C
2 A = 180º
(Angle sum property of a triangle)
F
H
G
I
K
J A
180º
2
90º .
 One of the angles of the triangle is a
right angle.
Hence, the triangle is a right triangle.
Q. 7. In a ABC, if 3 A = 4 B = 6 C,
calculate the angles.
Sol. In a ABC,
.
.
.
 3 A = 4 B = 6 C = 1  (say)
A =
1
3
B =
1
4
C =
1
6
 Ratio 
1
3
1
4
1
6
: :
 
4 3 2
12
: :
(LCM of 3, 4, 6 = 12)
= 4 : 3 : 2
Sum of angles ABC = 180º
 A =
180º 4
4 + 3 + 2
180 4
9
80
º
º
     B =
180º 3
9
60º
     
C =
180º 2
9
40º
Hence, angles of ABC are 80º, 60º and 40º.   Ans.
Q. 8. Look at the figure given below. State
for each triangle whether it is acute, right
or obtuse.
Sol. (i) It is obtuse triangle.
(ii) It is acute triangle.
(iii) It is right triangle.
(iv) It is obtuse triangle.
Q. 9. In the given figure some triangles have
been given. State for each triangle
whether it is scalene, isosceles or
equilateral.
C B
130°
A
60°
60° 60°
E F
D
Q R
P
90°
92°
Y Z
X
Sol. (i) It is an isosceles triangle as it has
two equal sides.
(ii) It is an isosceles triangle as it has two
equal sides.
(iii) It is a scalene triangle as its sides are
different in length.
(iv) It is an equilateral triangle as its all sides
are equal.
(v) It is an equilateral triangles as its angles
are equal, so its sides will also be equal.
(vi) It is an isosceles triangle as its two base
angles are equal, so its two sides are equal.
(vii) It is a scalene triangle as its angles are
different, so its sides will also be different
or unequal.
Q.10. Draw a ABC. Take a point D on
BC. Join AD
How many triangles do you get ? Name
them.
C B
A
D
Sol. In ABC, D is a point on BC and AD
is joined
Now we get triangles ABC, ABD
and ADC
Q. 11. Can a triangle have :
(i) Two right angles
(ii) Two obtuse angles
(iii) Two acute angles
(iv) Each angles more than 60º
(v) Each angles less than 60º
(vi) Each angles equal to 60º
Sol. (i) No (ii) No    (iii) Yes
(iv) No            (v) No    (vi) Yes.
Q. 12. Fill in the blanks :
(i) A triangle has ............ sides, ............
angles and ............ vertices.
(ii) The sum of the angles of a triangle
is............ .
(iii) The sides of a scalene triangle are of
............ lengths.
(iv) Each angle of an equilateral triangle
measures............ .
(v) The angles opposite to equal sides of an
isosceles triangle are............ .
(vi) The sum of the lengths of the sides of a
triangle is called its............ .
Sol. (i) three, three, three.
(ii) 180º       (iii) different        (iv) 60º
(v) equal       (vi) perimeter.
( ) EXERCISE 16 B
Objective questions
Mark ( ) against the correct answer
in each of following.
Q. 1. How many parts does a triangle have ?
(a) 2 (b) 3
(c) 6 (d) 9
Sol. (c) 
.
.
.
 It has three sides and three angles
i.e. six.
Q. 2. With the angles given below, in which
case the construction of triangle is
possible?
L (a) 30º, 60º, 70º (b) 50º, 70º, 60º
(c) 40º, 80º, 65º (d) 72º, 28º, 90º
Sol. (b) 
.
.
.
 Sum of three angles of a triangle is
180º.
Q. 3. The angles of a triangle are in the ratio
2 : 3 : 4. The largest angle is
(a) 60º (b) 80º
(c) 76º (d) 84º
Sol. (b) 
.
.
.
 Largest angle
180 4
2 3 4
180 4
9
80
º º
º
.
Q. 4. The two angles of a triangle are
complementary. The third angle is
(a) 60º (b) 45º
(c) 36º (d) 90º
Sol. (d) 
.
.
.
 A triangle has 180º and if two
angles are complementary i.e. sum of
two angles is 90º, then third angle will be
180º – 90º = 90º.
Q. 5. One of the base angles of an isosceles
triangle is 70º The vertical angle is
(a) 60º (b) 80º
(c) 40º (d) 35º
Sol. (c) 
.
.
.
 Sum of three angles is 180º and
sum of two equal angles = 70º + 70º =
140º, then third angle will be 180º – 140º
= 40º.
Q. 6. A triangle having sides of different lengths
is called
(a) an isosceles triangle
(b) an equilateral triangle
(c) a scalene triangle
(d) a right triangle
Sol. (c) 
.
.
.
 A scalene triangle has different
sides.
Q.7. In an isosceles ABC, the bisectors of
B and C meet at a point O. If A
= 40º, then BOC = ?
(a) 110º (b) 70º
(c) 130º (d) 150º
Sol. In an isosceles ABC, B = C
and bisector of B and C meet at O
and A = 40º
O
A
40º
B C
B = C = 
2
º 40 º 180
= 
2
º 140
 = 70º
2
1
B = 
2
1
C = 
2
º 70
 = 35º
Now in OBC
BOC + OBC + OCB = 180º
BOC + 
2
1
B + 
2
1
C = 180º
BOC + 35º + 35º = 180º
BOC = 180º – 70º = 110º (a)
Q.8. The side of a triangle are in the ratio
3 : 2 : 5 and its perimeter is 30 cm. The
length of the longest side is
(a) 20 cm (b) 15 cm
(c) 10 cm (d) 12 cm
Sol. Side of a trianlge are in the ratio 3 : 2 : 5
and perimter = 30 m
Length of longest side = 
5 2 3
5 30
= 
10
5 30
 cm = 15 cm (b)
Q.9. Two angles of a trianlge measure 30º and
25º respectively. The measure of the third
angle is
(a) 35º (b) 45º
(c) 65º (d) 125º
Sol. Two angles of a trianlge are 30º and 25º
But sum of three angles of a triangle
= 180º
Third angle = 180º – (30 + 25º)
= 180º – 55º = 125º (d)
Q.10. Each angle of an equilateral triangle
measures
(a) 30º (b) 45º
(c) 60º (d) 80º
Sol. Each angles of an equilateral triangle
= 60º
as each angle of an equilateral triangle
are equal
Each angle = 
3
º 180
 = 60º (c)
Q. 11. In the adjoining figure, the point P lies
(a) in the interior of ABC
(b) in the exterior of ABC
(c) on ABC (d) outside ABC
C
A
B
P
Sol. _ In the figure, P lies on AB
Its lies on the ABC (c)