Question

You can represent the measures of an angle and its complement as x° and (90 − x)°. Similarly, you can represent the measures of an angle and its supplement as x° and (180 − x)°. Use these expressions to find the measures of the angles described. The measure of an angle increased by 58° is equal to the measure of its complement.

Answer 1

180° - x = 5 · ( 90° - x )

180° - x = 450° - 5 x

5 x - x = 450° - 180°

4 x = 270°

x = 270° : 4

x = 67.5°

The measure of an angle is 67.5°.

Its complement angle: 22.5°.

Its supplement angle: 112.5°

112.5° = 5 x 22.5

Explanation: