Let the measure of the angle be \( x \) degrees. The measure of its supplementary angle will then be \( 180 - x \) degrees, since supplementary angles add up to \( 180 \) degrees.
According to the problem, the measure of the angle \( x \) is seventy-one times the measure of its supplementary angle. We can express this relationship with the following equation:
\[ x = 71(180 - x) \]
Now, we'll solve for \( x \).
- Distribute \( 71 \) on the right side of the equation:
\[ x = 71 \times 180 - 71x \] \[ x = 12780 - 71x \]
- Next, we will add \( 71x \) to both sides to get all the terms involving \( x \) on one side:
\[ x + 71x = 12780 \] \[ 72x = 12780 \]
- Now, divide both sides by \( 72 \):
\[ x = \frac{12780}{72} = 177.5 \]
- Now we find the measure of the supplementary angle:
\[ 180 - x = 180 - 177.5 = 2.5 \]
Thus, the measures of the angles are:
- \( x = 177.5 \) degrees (the angle)
- \( 180 - x = 2.5 \) degrees (the supplementary angle)
To summarize, the measure of the angle is \( 177.5 \) degrees and the measure of the supplementary angle is \( 2.5 \) degrees.