Question

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.

Answer 1

x = 35

77 degrees

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!

Answer 2

• x = 35°
• 77

Explanation:

Supplementary angles add up to 180°

• 3x - 2° + 2x + 7° = 180°
• 5x + 5° = 180°
• 5x = 175°
• x = 35°

Angles

• 3*35° - 2° = 105° - 2° = 103°

and

• 180° - 103° = 77°