Question

The difference between the measures of the two angles of a complementary pair is ${40}^{\circ }$. Find the measures of the two 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 ${90}^{\circ }-x^{\circ }$

According to the statement,

$\Rightarrow x^{\circ }-({90}^{\circ }-x^{\circ })={40}^{\circ }$

$\Rightarrow x^{\circ }-{90}^{\circ }+x^{\circ }={40}^{\circ }$

$\Rightarrow 2x^{\circ }={40}^{\circ }+{90}^{\circ }={130}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{130}^{\circ }}{2}={65}^{\circ }$.

Hence, the measure of the angle is $x={65}^{\circ }$

and its complement is ${90}^{\circ }-x={90}^{\circ }-{65}^{\circ }={25}^{\circ }$