Question

an angle measures 136° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Let \( x \) be the measure of the angle we want to find. The supplementary angle, by definition, is \( 180^\circ - x \).

According to the problem, the angle measures 136 degrees more than its supplementary angle. Therefore, we can set up the following equation:

\[
x = (180^\circ - x) + 136^\circ
\]

Now, we will simplify and solve this equation:

1. Distribute and simplify:
\[
x = 180^\circ - x + 136^\circ
\]

2. Combine like terms:
\[
x = 316^\circ - x
\]

3. Add \( x \) to both sides:
\[
2x = 316^\circ
\]

4. Divide by 2:
\[
x = 158^\circ
\]

Now that we have found the measure of the angle, we can find its supplementary angle:

\[
180^\circ - x = 180^\circ - 158^\circ = 22^\circ
\]

Thus, the measures of the angles are:
- The angle: \( 158^\circ \)
- Its supplementary angle: \( 22^\circ \)

In conclusion, the two angle measures are \( 158^\circ \) and \( 22^\circ \).