Question

Two supplementary angles are in the ratio of 5 to 7. Find positive difference of the measure of the two angles. Do the same problem, only do it for complementary angles instead of supplementary angles.​

Answer 1

30° is the difference if they are supplement

15° is the difference if they are complementary

Explanation:

Let 5x = the measure of the smaller angle

and 7x = the measure of the larger angle

If they are supplementary, then 5x + 7x = 180

12x = 180

x = 15

5x = 5(15) = 75 = the measure of the smaller angle

7x = 7(15) = 105 = the measure of the larger angle

105 - 75 = 30 = difference of the measures

Now, if they are complementary, then 5x + 7x = 90

12x = 90

x = 7.5

5x = 7(7.5) = 37.5 = the measure of the smaller angle

7x = 7(7.5) = 52.5 = the measure of the larger angle

52.5 - 37.5 = 15 = difference of the measures