Question

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

Answer 1

Step 1: Define angles.

Let the smaller angle be \( x \). The larger angle is \( x + 18^\circ \).

Step 2: Apply supplementary angle property.

The sum of supplementary angles is \( 180^\circ \). Form the equation:
\[x + (x + 18^\circ) = 180^\circ\]

Step 3: Solve the equation.

Simplify the equation:
\[x + x + 18^\circ = 180^\circ\]\[2x + 18^\circ = 180^\circ\]Subtract \( 18^\circ \) from both sides:
\[2x = 162^\circ\]Divide by 2:
\[x = \frac{162^\circ}{2} = 81^\circ\]

Step 4: Calculate the larger angle.

The smaller angle is \( 81^\circ \). The larger angle is:
\[81^\circ + 18^\circ = 99^\circ\]

Step 5: State the angles.

The smaller angle is \( 81^\circ \), and the larger angle is \( 99^\circ \).