Question

Find the measure of an angle if five times its complement is 12° less than twice its supplement.

Answer 1

Let the measure of the angle be x$°$.
Then, its complement = ${\left(90-x\right)}^{\circ }$
And its supplement = ${\left(180-x\right)}^{\circ }$
$$\begin{gathered} \Rightarrow 5\left(90-x\right)=2\left(180-x\right)-12 \\ \Rightarrow 450-5x=360-2x-12 \\ \Rightarrow 450-348=3x \\ \Rightarrow 3x=102 \\ \Rightarrow x=34 \end{gathered}$$
Therefore, the measure of the required angle is ${34}^{\circ }$.