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

1.	The measures of some angles are given below. Write the measures of their complementary angles.i. 20° ii. 90° iii. x°
Answer» i. 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°. ii. 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°. iii. 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)°.

The measures of some angles are given below. Write the measures of their complementary angles.i. 20° ii. 90° iii. x°

Answer»

i. 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°.

ii. 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°.

iii. 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)°.