Beginning Algebra, 11th Edition

Finding the Measure of an Angle

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

Step 1 Readthe problem. We must find the measure of an angle, given information

about the measure of its complement.

Step 2 Assign a variable.

Let the degree measure of the angle.

Then the degree measure of its complement.

Step 3 Write an equation.

Measure of the 5 times the measure

complement is of the angle.

5 x

Step 4 Solve. Add x.

Combine like terms.

Divide by 6.

,or

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

Step 6 Check. If the angle measures , then its complement measures

, which is equal to five times , as required.

NOW TRY

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

Then

and

We can visualize this information using a sketch. See FIGURE 6.

180 - x= the degree measure of its supplement.

90 - x= the degree measure of its complement,

x= the degree measure of the angle.

EXAMPLE 9

90°- 15°= 75° 15°

15°

15°

15 =x x= 15

90

6

=

6 x

6

90 = 6 x

90 - x+x= 5 x+x

90 - x =

90 - x=

x=

EXAMPLE 8

114 CHAPTER 2 Linear Equations and Inequalities in One Variable

If xrepresents the degree measure of an angle, then

180 x represents the degree measure of its supplement.

90 x represents the degree measure of its complement.

PROBLEM-SOLVING HINT

NOW TRY
EXERCISE 8
Find the measure of an angle
whose complement is twice
its measure.

x

Complement

of x:

90 2 x

xx x x

Supplement of x:

180 2 x

x

FIGURE 6

NOW TRY ANSWER

8. 30°

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