The measures of two supplementary angles are in the ratio 2:3. Find the measure of the larger angle.
A) 36°
B) 54°
C) 72°
D) 108°

Question

Quizplus · Accepted Answer

Let x be the measure of the smaller angle in degrees, then the larger angle measures 180° - x. According to the problem, we have:

(180° - x)/x = 3/2

Cross-multiplying gives:

2(180° - x) = 3x

Simplifying the equation by expanding the left side gives:

360° - 2x = 3x

Adding 2x to both sides gives:

360° = 5x

Dividing both sides by 5 gives:

x = 72°

Therefore, the larger angle measures:

180° - x = 180° - 72° = 108°

So the answer is (D) 108°.

The Measures of Two Supplementary Angles Are in the Ratio