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QUESTION: 1

An exterior angle of a triangle is 80^{°}and two interior opposite angles are equal. Measure of each of these angles is :

Solution:

Exterior angle = sum of two interior opposite angle so, exterior angle =1/2×80 = 40^{°}

QUESTION: 2

An exterior angle of a triangle is 80^{0} and the interior opposite angles are in the ratio 1 : 3. Measure of each interior opposite angle is :

Solution:
X+3x=80(exterior angle of triangle is equal to two interior opposite angles) 4x=80 x=80/4 x=20 So, x=20 and 3x=3*20=60 are two opposite interior angles.

QUESTION: 3

In the adjoining figure, if m ║ n, then ∠4 + ∠7 is equal to –

Solution:

QUESTION: 4

If two angles are supplementary and the larger is 20^{0} less then three times the smaller, then the angles are :-

Solution:

supplementary = 180 degrees

larger = 3x - 20

smaller = x

3x - 20 + x = 180

4x - 20 = 180

4x = 180 + 20

4x = 200

4x/4 = 200/4

x = 50

smaller = 50 degrees

larger = 3(50) - 20 = 150 - 20 = 130 degrees

QUESTION: 5

In the given figure, ∠BAC = 40^{0}, ∠ACB = 90^{0} and ∠BED = 100^{0}, Then ∠BDE = ?

Solution:

QUESTION: 6

The angle which is equal to 8 times its complement is :

Solution:

QUESTION: 7

Two planes intersect each other to form a :

Solution:
Two non-parallel planes in space form a line upon intersection, as long as each plane is unique. Three non-parallel planes intersect at a point. The best and simplest example is to fold a piece of paper. Since the folded paper now represents two distinct planes, the crease itself is the intersection point, forming a line.

QUESTION: 8

In the adjoining figure, m ║ n, if ∠1 = 50^{0}, then ∠2 is equal to –

Solution:

QUESTION: 9

In a right-angled triangle where angle A = 90° and AB = AC. What are the values of angle B?

Solution:

∵ In ∆ABC,

AB = AC

∴ ∠B = ∠C ...(1)

| Angles opposite to equal sides of a triangle are equal

In ∆ABC,

∠A + ∠B + ∠C = 180°

| Sum of all the angles of a triangle is 180°

⇒ 90° + ∠B + ∠C = 180°

| ∵ ∠A = 90° (given)

⇒ ∠B + ∠C = 90° ...(2)

From (1) and (2), we get

∠B = ∠C = 45°.

QUESTION: 10

In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50^{0}, then ∠BOC = ?

Solution:

a+b+c = 180

50+b+c= 180

b+c = 130 ............(1)

divide equation (1) by 2

1/2(b+c) = 65...........(2)

now in triangle obc

o+1/2(b+c) = 180

o+65= 180 ( from (2))

o= 180-65= 115

QUESTION: 11

An exterior angle of a triangle is 80^{0} and the interior opposite angles are in the ratio 1 : 3. Measure of each inte4rior opposite angle is :

Solution:

Let the interior angles be x and 3x

We know that exterior angle of triangle is equal to sum of interior opposite angles.

⇒ x+3x=80^{∘}

⇒ 4x=80^{∘}

⇒ x=20^{∘}

So the angles are

x=20^{∘}

3x=3×20^{∘}

= 60∘

QUESTION: 12

In figure, AB and CD are parallel to each other. The value of x is :

Solution:

QUESTION: 13

In the adjoining figure, m ║ n. If ∠a : ∠b = 2 : 3, then the measure of ∠h is –

Solution:

A+b =180(linear pair)

2x+3x=180

5x=180

x=180/5

x=36

a=2x=2*36=72

b=3x=3*36=108

b=d (vertical opposite angles are equal)

d=f (alternative interior angles are equal)

f=h (vertically opposite angles are equal)

So, h= 108

QUESTION: 14

In the given figure, the measure of ∠ABC is :

Solution:

QUESTION: 15

In the given figure, AB ∥ CD. If ∠EAB = 50^{0} and ∠ECD = 60^{0}, then ∠AEB = ?

Solution:

QUESTION: 16

In the given figure, the value of x which makes POQ a straight line is :

Solution:
2x+ 30+ 4x = 180 6x = 150 x = 25

QUESTION: 17

In two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the smaller of the two angles is :

Solution:

QUESTION: 18

In the adjoining figure, AB ║ CD and AB ║ EF. The value of x is :-

Solution:

Given, AB ║ CD and AB ║ EF

so CD || EF

which means ∠ECD + ∠CEF = 180^{0} (corresponding angles)

∠ECD = 180 - 150 = 30^{0}

since AB || CD so

∠ABC= ∠BCD (alternate interior angles)

∠ABC = 30 + ∠ECD = 30 + 30 = 60^{0}

QUESTION: 19

In the adjoining figure, the bisectors of ∠CBD and ∠BCE meet at the point O. If ∠BAC = 70^{0}, then ∠BOC is equal to :-

Solution:

QUESTION: 20

In the given figure, ∠OEB = 75^{0}, ∠OBE = 55^{0} and ∠OCD = 100^{0}. Then ∠ODC = ?

Solution:

QUESTION: 21

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the largest of two angles is :

Solution:

QUESTION: 22

Sum of all angles around a main point equals to

Solution:

QUESTION: 23

What is the supplement of 105°

Solution:

QUESTION: 24

In the adjoining figure, BE and CE are bisectors of ∠ABC and ∠ACD respectively. If ∠BEC = 25^{0}, then ∠BAC is equal to :-

Solution:

QUESTION: 25

Find the angle if six times of its complement 12° less than twice of its supplement?

Solution:

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