Question

The measure of the supplementary of an angle is 20^°  more than four times of original angle. Find the complementary angle of that particular angle?
1. 58^° 
2. 50^° 
3. 30° 
4. 32^° 

Answer 1

Correct Answer - Option 1 : 58^° 

Given:

The supplementary of an angle is 20^° more than four times of original angle

Concept used:

Two angles are called complementary when their measures add to 90 degrees.

Two angles are called supplementary when their measures add up to 180 degrees.

Calculation:

Let the original angle be x

Its supplementary angle = 4x + 20° 

According to the question,

⇒ x + 4x + 20° = 180°

⇒ 5x = 160° 

⇒ x= 160°/5

⇒ x = 32^°

Its complementary angle = 90° – 32° = 58° 

∴ The complementary angle of that particular angle is 58°