Home
>
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 $\alpha$ and $\beta$ are said to be complementary angles if $\alpha +\beta =90°$.Given, an angle is equal to $8$ times of its complement. Let the given angle be $\alpha$ and let $\beta$ be its complementary angle, then$\alpha =8\beta$Since $\alpha$ and $\beta$ are complementary angles, therefore$\begin{array}{rcl}\alpha +\beta & =& 90°\\ & ⇒& 8\beta +\beta =90°\left[\because \alpha =8\beta \right]\\ & ⇒& 9\beta =90°\\ & ⇒& \beta =10°\end{array}$Therefore, $\begin{array}{rcl}\alpha & =& 8\beta \\ & =& 8\left(10°\right)\\ & =& 80°\end{array}$Hence, the measure of the given angle is $80°$.MathematicsStandard IX

Suggest Corrections
0