Question

The difference between the angle and its complement is ${36}^{\circ }$. Find the angles.

Answer 1

We know, two angles are said to be complementary, if the sum of their measures is ${90}^{\circ }.$

Let the angle be $x^{\circ }$ and its complement is ${90}^{\circ }-x^{\circ }$

Then, according to the statement,

$\Rightarrow x^{\circ }-({90}^{\circ }-x^{\circ })={36}^{\circ }$

$\Rightarrow x^{\circ }-{90}^{\circ }+x^{\circ }={36}^{\circ }$

$\Rightarrow 2x^{\circ }={36}^{\circ }+{90}^{\circ }={126}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{126}^{\circ }}{2}={63}^{\circ }$.

Hence, the measure of the angle is ${63}^{\circ }$ and its complement is ${27}^{\circ }$.