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:

\[ 81^\circ + 18^\circ = 99^\circ \]