Question

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

i. 20° 

ii. 90° 

iii. x°

Answer 1

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)°.