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.
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