Question 1.

The measures of some angles are given below. Write the measures of their complementary angles.

i. 40°

ii. 63°

iii. 45°

iv. 55°

v. 20°

vi. 90°

vii. x°

Solution:

i. Let the measure of the complementary angle be x°.

∴ 40 + x = 90

∴ 40 + x – 40 = 90 – 40

….(Subtracting 40 from both sides)

∴ x = 50

∴ The measure of the complement of an angle of measure 40° is 50°.

ii. Let the measure of the complementary angle be x°.

∴ 63 + x = 90

∴ 63+x-63 = 90-63

….(Subtracting 63 from both sides)

∴ x = 27

∴ The measure of the complement of an angle of measure 63° is 27°.

iii. Let the measure of the complementary angle be x°.

∴ 45 + x = 90

∴ 45+x-45 = 90-45

….(Subtracting 45 from both sides)

∴ x = 45

∴ The measure of the complement of an angle of measure 45° is 45°.

iv. Let the measure of the complementary angle be x°.

∴ 55 + x = 90

∴ 55 + x-55 = 90-55

….(Subtracting 55 from both sides)

∴ x = 35

∴ The measure of the complement of an angle of measure 55° is 35°.

v. Let the measure of the complementary angle be x°.

∴ 20 + x = 90

∴ 20 + x – 20 = 90 – 20

….(Subtracting 20 from both sides)

∴ x = 70

∴ The measure of the complement of an angle of measure 20° is 70°.

vi. Let the measure of the complementary angle be x°.

∴ 90 + x = 90

∴ 90 + x – 90 = 90 – 90

….(Subtracting 90 from both sides)

∴ x = 0

∴ The measure of the complement of an angle of measure 90° is 0°.

vii. Let the measure of the complementary angle be a°.

∴ x + a = 90

∴ x + a – x = 90 – x

….(Subtracting x from both sides)

∴ a = (90 – x)

∴ The measure of the complement of an angle of measure x° is (90 – x)°.

Question 2.

(y – 20)° and (y + 30)° are the measures of complementary angles. Find the measure of each angle.

Solution:

(y – 20)° and (y + 30)° are the measures of complementary angles.

∴ (y – 20) + (y + 30) = 90

∴ y + y + 30 – 20 = 90

∴ 2y+10 = 90

∴ 2y = 90 – 10

∴ 2y = 80

∴ *y*=80/2

= 40

Measure of first angle = (y – 20)° = (40 – 20)° = 20°

Measure of second angle = (y + 30)° = (40 + 30)° = 70°

∴ The measure of the two angles is 20° and 70°.

**Intext Questions and Activities**

Question 1.

Observe the angles in the figure and enter the proper number in the empty place. (Textbook pg. no. 26)

- m∠ABC = ___°.
- m∠PQR = ___°.
- m∠ABC + m∠PQR = ___°.

Solution:

- 40
- 50
- 90

Note: Here, the sum of the measures of ∠ABC and ∠PQR is 90 °. Therefore, they are complementary angles.