An angle is equal to 8 times its complement. Determine its measure.


Given:

An angle is equal to 8 times its complement.

To do:

We have to find the measure of the angle.

Solution:

Two angles are said to be complementary if the sum of their measures is $90^o$.

Let the required angle be $x$.

This implies,

The measure of the complementary angle $=90^o-x$

According to the question,

$x=8(90^o-x)$

$x=720^o-8x$

$x+8x=720^o$

$9x=720^o$

$x=\frac{720^o}{9}$

$x=80^o$

The measure of the required angle is $80^o$.

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Updated on: 10-Oct-2022

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