Question

The greater of two supplementary angles exceeds the smaller by $18^\circ$. Find the measures of these two angles.

Answer 1

Let the smaller angle be $x$. Then, the larger angle is $x + 18^\circ$.

Since the angles are supplementary, their sum is $180^\circ$:

$x + (x + 18^\circ) = 180^\circ$

Simplifying:

$2x + 18^\circ = 180^\circ \implies 2x = 162^\circ \implies x = 81^\circ$

Thus, the smaller angle is $81^\circ$, and the larger angle is:

$81^\circ + 18^\circ = 99^\circ$