Question

3)Two supplementary angles have the property that the measure of the larger angle is four times the measure of the smaller angle. Which of the following are the two angle measures? Show all work (1) 18º and 72° (2) 25° and 100° (3) 30° and 120° (4) 36° and 144°

Answer 1

If the smaller angle is x and the larger is 4 times the smaller the the larger is 4x. Given that both angles are supplementary then

x + 4x = 180 (Supplementary angles add up to 180)

5x = 180

Divide both sides by

5x/5 = 180/5

x = 36

the larger angle will be

= 4 * 36

= 144

Hence the angles are 36° and 144°​.

(4) 36° and 144°​