Basic Mathematics for College Students

Chapter 9 Summary and Review 813

Vertical angles are congruent (have the same
measure).

Refer to the figure below. Find and x m(XYZ).

When two lines intersect, pairs of nonadjacent angles Vertical angles
are called vertical angles.

X

R

Z

T

Y

3 x + 20 °

2 x + 70 °

Since the angles are vertical angles, they have equal measures.

Set the expressions equal.

Eliminate 2xfrom the right

side.

Combine like terms.

Subtract 20° from both sides.

Thus, is 50°. To find , evaluate the expression

for.

Substitute 50° for x.

Do the multiplication.

Do the addition.

Thus,m(XYZ)170°.

170°

150°20°

3 x20°3( 50 °)20°

3 x20° x50°

x m(XYZ)

x50°

x20°70°

3 x20° 2 x 2 x70° 2 x

3 x20° 2 x70°

If the sum of two angles is 90°, the angles are
complementary.

If the sum of two angles is 180°, the angles are
supplementary.

63°  27° 90° 146°  34° 180°

27°

63°

146°

34°

Complementary angles Supplementary angles

We can use algebra to find the complement of an
angle.

Find the complement of an 11° angle.

Let the measure of the complement (in degrees).

The sum of the angles’ measures must be 90°.

To isolate x,subtract 11° from both sides.

The complement of an 11° angle has measure 79°.

x79°

x11°90°

x

We can use algebra to find the supplement of an
angle.

Find the supplement of a 68° angle.

Let the measure of the supplement (in degrees).

The sum of the angles’ measures must be 180°.

To isolate x,subtract 68° from both sides.

The supplement of a 68° angle has measure 112°.

x112°

x68°180°

x