Question

The difference in the measures of the two complementary angles is ${12}^o$. Find the measure of 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,

$\Rightarrow x^{\circ }-({90}^{\circ }-x^{\circ })={12}^{\circ }$

$\Rightarrow x^{\circ }-{90}^{\circ }+x^{\circ }={12}^{\circ }$

$\Rightarrow 2x^{\circ }={12}^{\circ }+{90}^{\circ }={102}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{102}^{\circ }}{2}={51}^{\circ }$.

Hence, the measure of the angle is $x={51}^{\circ }$

and its complement is ${90}^o-x={90}^o-{51}^o={39}^{\circ }$.