Question

Find the measure of an angle whose supplement is sixteen times its complement. Hint: Supplement and complement of an angle are (180-0) and (90-0) respectively.

Answer 1

84⁰

Explanation:

Complement = 90 - x

Supplement = 180 - x

Given:

180 - x = 16(90 - x)

180 - x = 1440 - 16x

15x = 1260

x = 84

Answer 2

The angle is 84 degrees

Explanation:

Let's call the angle by 'x'.

the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.

If the supplement is sixteen times the complement, we can write the following equation:

(180 - x) = 16 * (90 - x)

180 - x = 1440 - 16x

16x - x = 1440 - 180

15x = 1260

x = 84

The angle is 84 degrees.