Question

Among the two supplementary angles the measure of the larger angle is ${36}^{\circ }$ more than the measure of smaller. Find the measures of the angles.

Answer 1

Let $x$ be measure of the smaller angle, then

$x+{36}^{\circ }$ will be the measure of the larger angle.

Thus, $x+x+{36}^{\circ }={180}^{\circ }$ [The sum of angles will be ${180}^{\circ }$, as the angles are supplementary]

$\Rightarrow 2x+{36}^{\circ }={180}^{\circ }$

$\Rightarrow 2x={144}^{\circ }$

$\Rightarrow x={72}^{\circ }$ (smaller angle)

Larger angle: $x+{36}^{\circ }={72}^{\circ }+{36}^{\circ }={108}^{\circ }$ (larger angle)