Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma MCQs: Triangle and its Angles
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Page 1
Question:41
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
a
90°
b
45°
c
60°
d
30°
Solution:
In a given ?ABC we are given that the three angles are equal. So,
According to the angle sum property of a triangle, in ?ABC
Therefore, all the three angles of the triangle are equal to
So, the correct option is
c.
Question:42
If two acute angles of a right triangle are equal, then each acute is equal to
a
30°
b
45°
c
60°
d
90°
Solution:
In the given problem, we have a right angled triangle and the other two angles are equal.
So, In ?ABC
Page 2
Question:41
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
a
90°
b
45°
c
60°
d
30°
Solution:
In a given ?ABC we are given that the three angles are equal. So,
According to the angle sum property of a triangle, in ?ABC
Therefore, all the three angles of the triangle are equal to
So, the correct option is
c.
Question:42
If two acute angles of a right triangle are equal, then each acute is equal to
a
30°
b
45°
c
60°
d
90°
Solution:
In the given problem, we have a right angled triangle and the other two angles are equal.
So, In ?ABC
Now, using the angle sum property of the triangle, in ?ABC, we get,
( )
Therefore, the correct option is
b.
Question:43
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
a
75°
b
80°
c
40°
d
50°
Solution:
In the ?ABC, CD is the ray extended from the vertex C of ?ABC. It is given that the exterior angle of the triangle is and two of the interior opposite angles are equal.
So, and
.
So, now using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get.
In ?ABC
Therefore, each of the two opposite interior angles is
So, the correct option is
d.
Question:44
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
a
an isosceles triangle
b
an obtuse triangle
c
an equilateral triangle
d
a right triangle
Solution:
In the given problem, one angle of a triangle is equal to the sum of the other two angles.
Thus,
..........1
Now, according to the angle sum property of the triangle
In ?ABC
Page 3
Question:41
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
a
90°
b
45°
c
60°
d
30°
Solution:
In a given ?ABC we are given that the three angles are equal. So,
According to the angle sum property of a triangle, in ?ABC
Therefore, all the three angles of the triangle are equal to
So, the correct option is
c.
Question:42
If two acute angles of a right triangle are equal, then each acute is equal to
a
30°
b
45°
c
60°
d
90°
Solution:
In the given problem, we have a right angled triangle and the other two angles are equal.
So, In ?ABC
Now, using the angle sum property of the triangle, in ?ABC, we get,
( )
Therefore, the correct option is
b.
Question:43
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
a
75°
b
80°
c
40°
d
50°
Solution:
In the ?ABC, CD is the ray extended from the vertex C of ?ABC. It is given that the exterior angle of the triangle is and two of the interior opposite angles are equal.
So, and
.
So, now using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get.
In ?ABC
Therefore, each of the two opposite interior angles is
So, the correct option is
d.
Question:44
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
a
an isosceles triangle
b
an obtuse triangle
c
an equilateral triangle
d
a right triangle
Solution:
In the given problem, one angle of a triangle is equal to the sum of the other two angles.
Thus,
..........1
Now, according to the angle sum property of the triangle
In ?ABC
.........2
Further, using
2 in
1,
Thus,
Therefore, the correct option is
d.
Question:45
Side BC of a triangle ABC has been produced to a point D such that ?ACD = 120°. If ?B =
1
2
?A is equal to
a
80°
b
75°
c
60°
d
90°
Solution:
In the given problem, side BC of ?ABC has been produced to a point D. Such that and . Here, we need to find
Given
We get,
Now, using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
In ?ABC
Also,
Using1
Thus,
Therefore, the correct option is a
.
Question:46
In ?ABC, ?B = ?C and ray AX bisects the exterior angle ?DAC. If ?DAX = 70°, then ?ACB =
a
35°
b
90°
c
70°
d
55°
Solution:
In the given ?ABC, . D is the ray extended from point A. AX bisects and
Here, we need to find
Page 4
Question:41
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
a
90°
b
45°
c
60°
d
30°
Solution:
In a given ?ABC we are given that the three angles are equal. So,
According to the angle sum property of a triangle, in ?ABC
Therefore, all the three angles of the triangle are equal to
So, the correct option is
c.
Question:42
If two acute angles of a right triangle are equal, then each acute is equal to
a
30°
b
45°
c
60°
d
90°
Solution:
In the given problem, we have a right angled triangle and the other two angles are equal.
So, In ?ABC
Now, using the angle sum property of the triangle, in ?ABC, we get,
( )
Therefore, the correct option is
b.
Question:43
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
a
75°
b
80°
c
40°
d
50°
Solution:
In the ?ABC, CD is the ray extended from the vertex C of ?ABC. It is given that the exterior angle of the triangle is and two of the interior opposite angles are equal.
So, and
.
So, now using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get.
In ?ABC
Therefore, each of the two opposite interior angles is
So, the correct option is
d.
Question:44
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
a
an isosceles triangle
b
an obtuse triangle
c
an equilateral triangle
d
a right triangle
Solution:
In the given problem, one angle of a triangle is equal to the sum of the other two angles.
Thus,
..........1
Now, according to the angle sum property of the triangle
In ?ABC
.........2
Further, using
2 in
1,
Thus,
Therefore, the correct option is
d.
Question:45
Side BC of a triangle ABC has been produced to a point D such that ?ACD = 120°. If ?B =
1
2
?A is equal to
a
80°
b
75°
c
60°
d
90°
Solution:
In the given problem, side BC of ?ABC has been produced to a point D. Such that and . Here, we need to find
Given
We get,
Now, using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
In ?ABC
Also,
Using1
Thus,
Therefore, the correct option is a
.
Question:46
In ?ABC, ?B = ?C and ray AX bisects the exterior angle ?DAC. If ?DAX = 70°, then ?ACB =
a
35°
b
90°
c
70°
d
55°
Solution:
In the given ?ABC, . D is the ray extended from point A. AX bisects and
Here, we need to find
As ray AX bisects
Thus,
Now, according to the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
Thus,
Therefore, the correct option is
c.
Question:47
In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure of the other interior angle is
a
55°
b
85°
c
40°
d
9.0°
Solution:
In the given ?ABC, and
Now, according to the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
So,
Therefore, the correct option is
c.
Question:48
If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
a
90°
b
180°
c
270°
d
360°
Solution:
In the given ?ABC, all the three sides of the triangle are produced. We need to find the sum of the three exterior angles so produced.
Now, according to the angle sum property of the triangle
Page 5
Question:41
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
a
90°
b
45°
c
60°
d
30°
Solution:
In a given ?ABC we are given that the three angles are equal. So,
According to the angle sum property of a triangle, in ?ABC
Therefore, all the three angles of the triangle are equal to
So, the correct option is
c.
Question:42
If two acute angles of a right triangle are equal, then each acute is equal to
a
30°
b
45°
c
60°
d
90°
Solution:
In the given problem, we have a right angled triangle and the other two angles are equal.
So, In ?ABC
Now, using the angle sum property of the triangle, in ?ABC, we get,
( )
Therefore, the correct option is
b.
Question:43
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
a
75°
b
80°
c
40°
d
50°
Solution:
In the ?ABC, CD is the ray extended from the vertex C of ?ABC. It is given that the exterior angle of the triangle is and two of the interior opposite angles are equal.
So, and
.
So, now using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get.
In ?ABC
Therefore, each of the two opposite interior angles is
So, the correct option is
d.
Question:44
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
a
an isosceles triangle
b
an obtuse triangle
c
an equilateral triangle
d
a right triangle
Solution:
In the given problem, one angle of a triangle is equal to the sum of the other two angles.
Thus,
..........1
Now, according to the angle sum property of the triangle
In ?ABC
.........2
Further, using
2 in
1,
Thus,
Therefore, the correct option is
d.
Question:45
Side BC of a triangle ABC has been produced to a point D such that ?ACD = 120°. If ?B =
1
2
?A is equal to
a
80°
b
75°
c
60°
d
90°
Solution:
In the given problem, side BC of ?ABC has been produced to a point D. Such that and . Here, we need to find
Given
We get,
Now, using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
In ?ABC
Also,
Using1
Thus,
Therefore, the correct option is a
.
Question:46
In ?ABC, ?B = ?C and ray AX bisects the exterior angle ?DAC. If ?DAX = 70°, then ?ACB =
a
35°
b
90°
c
70°
d
55°
Solution:
In the given ?ABC, . D is the ray extended from point A. AX bisects and
Here, we need to find
As ray AX bisects
Thus,
Now, according to the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
Thus,
Therefore, the correct option is
c.
Question:47
In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure of the other interior angle is
a
55°
b
85°
c
40°
d
9.0°
Solution:
In the given ?ABC, and
Now, according to the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
So,
Therefore, the correct option is
c.
Question:48
If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
a
90°
b
180°
c
270°
d
360°
Solution:
In the given ?ABC, all the three sides of the triangle are produced. We need to find the sum of the three exterior angles so produced.
Now, according to the angle sum property of the triangle
.......
1
Further, using the property, “an exterior angle of the triangle is equal to the sum of two opposite interior angles”, we get,
......2
Similarly,
.......3
Also,
.......4
Adding
2
3 and
4
We get,
Thus,
Therefore, the correct option is
d.
Question:49
In ?ABC, if ?A = 100°, AD bisects ?A and AD ? BC. Then, ?B =
a
50°
b
90°
c
40°
d
100°
Solution:
In the given ?ABC, , AD bisects and .
Here, we need to find .
As, AD bisects ,
We get,
Now, according to angle sum property of the triangle
In ?ABD
Hence,
Therefore, the correct option is
c.
Question:50
An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are
a
48°, 60°, 72°
b
50°, 60°, 70°
c
52°, 56°, 72°
d
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Nov 24, 2024 Last updated |
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