Question

Find the measure of an angle, if seven times its complement is 10° less than three times its supplement.

Answer 1

Let the measure of the required angle be $x°$.
Then, the measure of its complement $=\left(90-x\right)°$.
And the measure of its supplement$=\left(180-x\right)°$.
Therefore,
$$\begin{gathered} 7\left(90-x\right)=3\left(180-x\right)-10 \\ \Rightarrow 630-7x=540-3x-10 \\ \Rightarrow 4x=100 \\ \Rightarrow x=25 \end{gathered}$$
Hence, the measure of the required angle is $25°$.