Question

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

i. 40° 

ii. 63°

iii. 45° 

iv. 55°

Answer 1

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°.