Solve the problem. See Examples.EXAMPLE Finding the Measure of an AngleFind the measure of...

Solve the problem. See Examples.

EXAMPLE Finding the Measure of an Angle

Find the measure of an angle whose complement is five times its measure.

Step 1 Read the problem. We must find the measure of an angle, given information about the measure of its complement.

Step 2 Assign a variable.

Step 3 Write an equation.

Step 4 Solve.

Step 5 State the answer. The measure of the angle is 15°.

Step 6 Check. If the angle measures 15°, then its complement measures 90° − 15° = 75°, which is equal to five times 15°, as required.

EXAMPLE Finding the Measure of an Angle

Find the measure of an angle whose supplement is 10° more than twice its complement.

Step 1 Read the problem. We are to find the measure of an angle, given information about its complement and its supplement.

Step 2 Assign a variable.

Let x = the degree measure of the angle.

Then 90 − x = the degree measure of its complement,

and 180 − x = the degree measure of its supplement.

We can visualize this information using a sketch. See FIGURE.

FIGURE

Step 3 Write an equation.

Step 4

Step 5 State the answer. The measure of the angle is 10°.

Step 6 Check. The complement of 10° is 80° and the supplement of 10° is 170°. 170° is equal to 10° more than twice 80° (that is, 170 = 10 + 2(80) is true). Therefore, the answer is correct.

Find the measure of an angle whose supplement is eight times its measure.