Answer:
The angle has measure 72°.
Explanation:
Definition:
Two angles are supplementary angles if the sum of their measures equals 180°.
Let x and y be the supplementary angles.
According to the definition above, then,
x + y = 180
We can the above equation for y:
x + y = 180
y = 180 - x
The two angles have measures:
x
180 - x
Now we look carefully at this statement:
"three times the measure of an angle is equal to twice the measure of the angle's supplement"
We translate the above statement into an equation, using x for one angle, and 180 - x for the supplement.
3x = 2(180 - x)
Solve the equation for x.
Distribute 2 on the right side.
3x = 360 - 2x
Add 2x to both sides.
5x = 360
Divide both sides by 5.
x = 360/5
x = 72
The angle has measure 72°.