Two angles are supplementary. One measure 3
x
−
2
and the other measures
2
x
+
7
. Find the value of x and the measure of the smaller angle.

Step-by-step explanation:

Supplementary angles add up to 180°

Angles

and

x = 35

77 degrees

Step-by-step explanation:

Supplementary angles mean that two angles add up to measure 180 degrees.

Solve for x.

(3x - 2) + (2x + 7) = 180

~Combine like terms

5x + 5 = 180

~Subtract 5 to both sides

5x = 175

~Divide 5 to both sides

x = 35

Angle 1:

3x - 2

3(35) - 2

105 - 2

103 degrees

Angle 2:

2x + 7

2(35) + 7

70 + 7

77 degrees

103 > 77

The smaller angle is 77.

Best of Luck!