Question

The measure of an angle is $6$ less than $5$ times its complement.

What is the measure of its complement

Answer 1

Finding the complement measure:

Two angles are complement to each other if their sum is $90°$.

Let the required angle be $x$ then its complement is $90-x$,

So, by the given data, the equation is

$\begin{array}{rcl}x& =& 5\times \left(90°-x\right)-6\\ x& =& 5\left(90°\right)-5x-6\\ x& =& 450°-5x-6\\ x+5x& =& 444°\\ 6x& =& 444°\\ x& =& \frac{444°}{6}\\ x& =& 72°\end{array}$

$\therefore$The angle is $72°$

Thus, the compliment is $90°-72°=18°$.

Hence, the complement measure is $18°$.