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 the supplement of an angle is five times the measure of its complement

Question

Mathematics

Haas

31 July, 21:05

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 the supplement of an angle is five times the measure of its complement

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Collin Cochran · 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°