Find the measures of the supplementary angles that satisfy each case.

Question

The measure of the first angle is 45 more than the second angle. What are the 2 angles?

Answer 1

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

Since the two angles are supplementary, their measures sum up to 180 degrees. Therefore, we can set up the following equation:

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

This simplifies to:

\[ 2x + 45 = 180 \]

Next, we can solve for \( x \):

1. Subtract 45 from both sides: \[ 2x = 180 - 45 \] \[ 2x = 135 \]

2. Divide by 2: \[ x = \frac{135}{2} \] \[ x = 67.5 \]

Now, we can find the first angle:

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

Thus, the measures of the two angles are:

• First angle: \( 112.5^\circ \)
• Second angle: \( 67.5^\circ \)

In conclusion, the two angles that are supplementary are:

\[ \text{First angle: } 112.5^\circ, \quad \text{Second angle: } 67.5^\circ \]