Basic Mathematics for College Students

816 Chapter 9 An Introduction to Geometry

(a) (b)

l 3

l 1 l 2

We can use algebra to find the unknown

measures of interior angles.

In the figure,. Find xand the

measure of each angle that is labeled.

Since the angles are interior angles

on the same side of the transversal,

they are supplementary.

The sum of the measures of two

supplementary angles is 180°.

Combine like terms.

Subtract 5° from both sides.

Divide both sides by 5.

Thus,xis 35°. To find the measures of the angles in the figure, we

evaluate the expressions for.

The measures of the angles labeled in the figure are 157° and 23°.

157°

140°17° 23°

4 x17°4(35°)17° x 12° 35 °12°

x35°

x35°

5 x175°

5 x5°180°

4 x17°x12°180°

l 1 l 2

l 1

l 2

4 x + 17°

x – 12°

17. a. Lines and shown in figure (a) below do not
    intersect and are coplanar. What word describes
    the lines?
    b. In figure (a), line intersects lines and in two
    distinct (different) points. What is the name
    given to line?
    c. What word describes the two lines shown in
    figure (b) below?

l 3

l 3 l 1 l 2

l 1 l 2

REVIEW EXERCISES

18. Identify all pairs of alternate interior angles shown
    in the figure below.

2 x − 30°

l 2 x^ + 10°

l 1

1 2

4 3

(^56)
(^87)

19. Refer to the figure in Problem 18. Identify all pairs
    of corresponding angles.

2 3

1

60° 4

50°

70°

E

DC

A B

22. In the figure on the right,
    . Find the measure of
    each angle that is labeled.


23. In the figure below,.
    a. Find x.
    b. Find the measure of each angle that is labeled.

l 1 l 2

DCAB

20. Refer to the figure in Problem 18. Identify all pairs
    of vertical angles.


21. In the figure below,. Find the measure of each
    angle.

l 1 l 2

54

67

110° 3

1 2

l 2

l 1