The supplement of an angle is six times as large as the complement of the angle. What is the measure of the angle to the nearest whole degree?

The measure of the angle to the nearest whole degree is 72 degrees

Solution:

Complementary angles add up to 90° and supplementary angles add up to 180°

Let "a" be the required angle

Supplement of an angle = 180 - a

Complement of angle = 90 - a

The supplement of an angle is six times as large as the complement of the angle.

Therefore,

180 - a = 6 (90 - a)

Simplify the above

180 - a = 540 - 6a

6a - a = 540 - 180

Combine the like terms

5a = 360

Divide both sides by 5

a = 72

Thus the measure of the angle to the nearest whole degree is 72 degrees