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QUESTION: 1

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: 2

In figure pair of alternate exterior angles arw :

Solution:

QUESTION: 3

What is the supplement of 105°

Solution:

Supplementary angles sums up to 180° x + 105° = 180° x=180° - 105° = 75°

QUESTION: 4

What is the measure of the complement of 45°?

Solution:

Complementary angle sums up to 90°. So x+ 45° = 90°

x = 90° - 45° = 45°

QUESTION: 5

What is the measure of the complement of 65^{Â°}?

Solution:

QUESTION: 6

What is the measure of the complement of 41^{Â°}?

Solution:

QUESTION: 7

What is the measure of the supplement of 54^{Â°}?

Solution:

QUESTION: 8

Identify which of the following pairs of angles are complementary.

Solution:

QUESTION: 9

Identify which of the following pairs of angles are supplementary.

Solution:

QUESTION: 10

Find the angle, which is equal to its complement.

Solution:

Complementary angles sums up to 90° since 45° + 45° = 90, 45 is complementary to itself

QUESTION: 11

Lines l║m, t is transversal then ∠ x ?

Solution:

QUESTION: 12

Find the angle, which is equal to its supplement.

Solution:

Supplementary angles sums up to 180° since 90° + 90° = 180°, 90° is supplementary to itself

QUESTION: 13

Lines l║m, t is transversal then ∠ x = ?

Solution:

120 and x are corresponding angles and corresponding angles are equal so x = 120^{°}

QUESTION: 14

Lines l║m, t is transversal then ∠ z = ?

Solution:

The angles are co-interior so x+60 = 180

x=120^{°}

QUESTION: 15

Lines l║m, t is transversal then ∠ x = ?

Solution:

QUESTION: 16

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Solution:

Given,

∠A = 90° and AB = AC

A/q,

AB = AC

⇒ ∠B = ∠C (Angles opposite to the equal sides are equal.)

Now,

∠A + ∠B + ∠C = 180° (Sum of the interior angles of the triangle.)

⇒ 90° + 2∠B = 180°

⇒ 2∠B = 90°

⇒ ∠B = 45°

Thus, ∠B = ∠C = 45°

QUESTION: 17

The measures of an angle supplement to the angle of 70° is ______.

Solution:

QUESTION: 18

Find the angle whose measure is five times its complement

Solution:

QUESTION: 19

Find x if I║m.

Solution:

QUESTION: 20

Find the value of x if I║m.

Solution:

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