If two angles are supplementary and the larger angle is 60 $^ { \circ }$ smaller than 2 times the smaller angle, find the measure of each angle.
A) 63 $^ { \circ }$ , 117 $^ { \circ }$
B) 105 $^ { \circ }$ , 75 $^ { \circ }$
C) 100 $^ { \circ }$ , 80 $^ { \circ }$
D) 110 $^ { \circ }$ , 70 $^ { \circ }$

Question

Quizplus · Accepted Answer

Let the smaller angle be x. Then the larger angle is 2x - 60 (since it is 60 degrees smaller than twice the smaller angle). 
Since the two angles are supplementary, we know that their sum is 180 degrees: 
x + (2x - 60) = 180 
Simplifying the equation: 
3x - 60 = 180 
3x = 240 
x = 80 
So the smaller angle is 80 degrees, and the larger angle is 2(80) - 60 = 100 degrees. Therefore, the answer is choice C.

If Two Angles Are Supplementary and the Larger Angle Is ∘^ { \circ }∘

If Two Angles Are Supplementary and the Larger Angle Is $^ { \circ }$