6th Grade Math Textbook, Fundamentals

Lesson 9-3 for exercise sets. &KDSWHU 

3UDFWLFH   $FWLYLWLHV

Use the diagram. Find the missing angle measures.

BECand CEDare complements. So 42° mCED90°.

CEDand DEFare supplements. So mCEDmDEF180°.

x

mCEDand y

mDEF

• To find the value of x:
  x 42  90 Write an equation.
  x 42  42  90  42

x 48

mCED 48

Subtract 42 from

both sides to

isolate x.

1

• To find the value of y:
  yx 180 Write an equation.
  y 48  180 Substitute 48 for x.
  y 48  48  180  48

y 132

mDEF 132

Subtract 48 from

both sides to

isolate y.

 are a pair of opposite angles

formed by two intersecting lines. Vertical

angles are congruent.

SVWand TVXare vertical angles.

So are SVTand WVX.

Vertical angles

SVW TVX

SVT WVX

W

ST

V

X

You can solve equations to find missing angle measures.

42°

F

A

B

C

D

x°

y°

E

Remember:

means “is congruent to”

Use the figure at the right for exercises 1–4.

1.Name an angle congruent to 1.

2.What is the measure of 4?

3.What angle is congruent to 4?

4.Which angles are supplements of 3?

Use the figure at the right for exercise 5.

5.Write and solve an equation for x.

For exercises 6–8, is the statement true? Write always, sometimes, or never.

6.If two angles are complements, they are acute angles.

7.If two angles are supplements, both are obtuse angles.

8.If two angles are adjacent and supplementary, one is a right angle.

9.Discuss and WriteAre adjacent angles always supplementary? Complementary?

Could they be either supplementary or complementary? Explain.

1

3

24

(3x  20)° x°

m 1 135°