Question

Find the measure of an angle which is ${30}^{\circ }$ less than its supplement.

Answer 1

Consider the required angle as $x^o$

We know that the complement can be written as ${180}^o-x^o$

To find the measure of an angle is equal to its complement

We get

$x^o=[{180}^o-x^o]+{30}^o$

We can also write it as

$x+x=90+36$

So we get

$2x=150$

By division we get

$x=\frac{150}{2}$

$x^o={75}^o$

Therefore the measure of an angle which is ${30}^o$ more than its complement is ${75}^o$