Question

Find the measures of the supplementary angles that satisfy each case. The measure of the first angle is 45 degrees more than the measure of the second

Answer 1

Let the measure of the second angle be \( x \) degrees. According to the problem, the measure of the first angle is \( 45 \) degrees more than the second angle, so we can express the first angle as \( x + 45 \) degrees.

Since these two angles are supplementary, their measures add up to \( 180 \) degrees. We can set up the following equation:

\[
x + (x + 45) = 180
\]

Simplifying the equation:

\[
2x + 45 = 180
\]

Subtracting \( 45 \) from both sides:

\[
2x = 135
\]

Dividing both sides by \( 2 \):

\[
x = 67.5
\]

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

\[
x + 45 = 67.5 + 45 = 112.5
\]

Thus, the measures of the supplementary angles are:

- First angle: \( 112.5 \) degrees
- Second angle: \( 67.5 \) degrees

So the supplementary angles are \( 112.5 \) degrees and \( 67.5 \) degrees.