The measure of an angle is thirty-five times 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 be \( 180 - x \) degrees.

According to the problem, the measure of the angle is thirty-five times the measure of its supplementary angle. We can set up the equation as follows:

\[ x = 35(180 - x) \]

Now, let's solve for \( x \):

1. Distribute on the right side:

\[ x = 6300 - 35x \]

2. Add \( 35x \) to both sides:

\[ x + 35x = 6300 \]

\[ 36x = 6300 \]

3. Divide both sides by 36:

\[ x = \frac{6300}{36} \]

Calculating the division:

\[ x = 175 \]

Now, let's find the measure of the supplementary angle:

\[ 180 - x = 180 - 175 = 5 \]

So, the measures of the angles are:

• The angle is \( 175 \) degrees.
• The supplementary angle is \( 5 \) degrees.

In conclusion, the measure of the angle is \( \boxed{175} \) degrees and the measure of its supplementary angle is \( \boxed{5} \) degrees.