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Question

An angle is one-fifth of its supplement. Find the measure of the angle.


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Solution

Supplementary angles:

When the sum of the measures of two angles is 180°, then the angles are called supplementary angles. When two angles are supplementary, each angle is said to be the supplement of the other.

Thus, two angles α and β are said to be supplementary angles, if α+β=180°.

Given, an angle is one-fifth of its supplement. Let the given angle be α and let β be its supplementary angle, then

α=15×βα=β5β=5α

Since α and β are supplementary angles, therefore

α+β=180°α+5α=180°β=5α6α=180°α=30°

Hence, the measure of the required angle is 30°.


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