Question

the measure of the supplement of an angle is three times the measure of the angle. find the measures of the angle and its supplement.
measure of the angle =
□°
measure of the angles supplement =
□°

Explanation:

Step1: Define the angle

Let the measure of the angle be \( x \) degrees.

Step2: Define the supplement

The supplement of the angle is \( 180 - x \) degrees (since supplementary angles add up to \( 180^\circ \)).

Step3: Set up the equation

We know that the supplement is three times the angle, so:
\( 180 - x = 3x \)

Step4: Solve for \( x \)

Add \( x \) to both sides:
\( 180 = 4x \)
Divide both sides by 4:
\( x = \frac{180}{4} = 45 \)

Step5: Find the supplement

The supplement is \( 3x = 3 \times 45 = 135 \) degrees.

Answer:

measure of the angle = \( 45^\circ \)
measure of the angle's supplement = \( 135^\circ \)