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An angle is equal to 8 times of its complement. Find its measure.
Question

An angle is equal to 8 times of its complement. Find its measure.


Solution

Complementary Angles :

When the sum of the measures of two angles is 90°, then the angles are called complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles.

Thus, two angles α and β are said to be complementary angles if α+β=90°.

Given, an angle is equal to 8 times of its complement. Let the given angle be α and let β be its complementary angle, then

α=8β

Since α and β are complementary angles, therefore

α+β=90°8β+β=90°α=8β9β=90°β=10°

Therefore,

α=8β=810°=80°

Hence, the measure of the given angle is 80°.


Mathematics
Standard IX

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