Question

Find the measure of an angle, if seven times its complement is ${10}^{\circ }$ less than three times its supplement.

Answer 1

Finding the value of x:

1. Two angles are called complementary if the sum of their measures is ${90}^o$.
2. Two angles are called supplementary if the sum of their measures is ${180}^o$.

Let the angle be $x^o$.
So complement angle will be ${(90-x)}^o$ and supplement angle will be ${(180-x)}^o$.

As per the question;
$7(90-x)=3(180-x)-10$
$4x=100$
$x=25$

Therefore, the value of x is ${25}^o$.
Hence, the measure of the required angle is ${25}^{\circ }$.