Question

An angle measures 116 degrees more than the measure of its supplementary angle. What is the measure of each angle

Answer 1

Let the measure of the angle be \( x \) degrees. The supplementary angle would then measure \( 180 - x \) degrees.

According to the given information, the angle measures 116 degrees more than its supplementary angle:

\[
x = (180 - x) + 116
\]

Now, simplify this equation:

\[
x = 180 - x + 116
\]
\[
x + x = 180 + 116
\]
\[
2x = 296
\]
\[
x = \frac{296}{2}
\]
\[
x = 148
\]

So, the angle measures \( 148 \) degrees.

Now, we can find the measure of the supplementary angle:

\[
180 - x = 180 - 148 = 32
\]

Thus, the measures of the angles are:
- The angle: \( 148 \) degrees
- The supplementary angle: \( 32 \) degrees.