Question

Two angles are complementary. The larger angle is $3^{\circ }$ less than twice the measure of the smaller angle. Find the measure of each angle.

Answer 1

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

Let $x$ be the measure larger angle and $y$ be the measure of smaller angle.

According to the given condition, $x=2y-3^{\circ }$...(i)

We know, $x+y={90}^{\circ }$,...(ii)

Substituting the value of $x$ from (i) in (ii),, we get,

$⟹$ $2y-3^{\circ }+y={90}^{\circ }$

$⟹$ $3y={93}^{\circ }$

$⟹$ $y={31}^{\circ }$.

$\therefore$ $x=2\left({31}^{\circ }\right)-3^{\circ }$ $={62}^{\circ }-3^{\circ }={59}^{\circ }$.

Hence, the smaller angle is ${31}^{\circ }$ and the larger angle is ${59}^{\circ }$.