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Lesson Menu

Five-Minute Check (over Chapter 10) Then/Now New

Vocabulary Key Concept Pairs of Angles Example

1 Find a Missing Angle Measure Key Concept

Names of Special Angles Example 2 Find

Measures of Angles Formed by Parallel

Lines Example 3 Use Algebra to Find Missing

Angle Measures

5-Minute Check 1

A. 5 B. 6 C. 7 D. 8

5-Minute Check 2

Which list of numbers is correctly ordered least

to greatest?

5-Minute Check 3

If c is the measure of the hypotenuse and a 6

and b 9, find the measure of c. Round to the

nearest tenth.

A. 10.5 units B. 10.8 units C. 11.3 units D. 12

units

5-Minute Check 4

Find the distance between A(3, 4), and B(5,

2). Round to the nearest tenth.

A. 8.2 units B. 8.1 units C. 8.0 units D. 7.9

units

5-Minute Check 5

What is the value of x? Classify the triangle by

its angles and by its sides.

A. 102 obtuse scalene B. 92 acute scalene

C. 90 right scalene D. 82 acute scalene

Then/Now

You have already found the missing angle measure

of a triangle. (Lesson 103)

- Examine relationships between pairs of angles.

- Examine relationships of angles formed by

parallel lines and a transversal.

Vocabulary

- perpendicular lines

- transversal

- vertical angles
- adjacent angles
- complementary angles
- supplementary angles
- parallel lines

- alternate interior angles
- alternate exterior angles
- corresponding angles

Concept A

Example 1 A

Find a Missing Angle Measure

A. Jun is cutting a tile. Classify the

relationship of ?a and ?b.

Answer The angles are complementary. The sum of

their measures is 90.

Example 1 B

Find a Missing Angle Measure

B. If m?a 53, what is the measure of ?b?

m?b 53 90 Write the equation. m?b

53 53 90 53 Subtract 53 from each side.

m?b 37 Simplify.

Answer m?b 37

Example 1 CYP A

A. Elisa is cutting a piece of fabric. What is

the relationship between ?a and ?b?

A. They are complementary. B. They are

supplementary. C. They are congruent. D. They are

obtuse.

Example 1 CYP B

B. If m?a 40, what is m?b?

A. 140 B. 220 C. 50 D. 90

Concept B

Example 2 A

Find Measures of Angles Formed by Parallel Lines

A. Classify the relationship between ?9 and ?13.

Answer Since ?9 and ?13 are corresponding

angles, they are congruent.

Example 2

Find Measures of Angles Formed by Parallel Lines

B. If m?13 is 75, find m?11 and m?15.

Since ?13 and ?11 are alternate interior

angles, they are congruent. So, m?11 75. ?11

and ?15 are corresponding angles and are

congruent. So, m?15 75.

Answer m?11 75 and m?15 75

Example 2 CYP A

A. What is the relationship between ?1 and ?5?

A. They are corresponding and congruent. B. They

are adjacent and supplementary. C. They are

corresponding and supplementary. D. They are

adjacent and congruent.

Example 2 CYP B

B. If m?3 78, what is m?7?

A. 12 B. 22 C. 78 D. 102

Example 3

Use Algebra to Find Missing Angle Measures

ALGEBRA Angles DEF and WXY are complementary

angles, with m?DEF 2x and m?WXY 3x 20.

Find the measures of ?DEF and ?WXY.

Step 1 Find the value of x.

m?DEF m?WXY 90 Complementary angles 2x

3x 20 90 Replace m?DEF with 2x and m?WXY

with 3x 20.

Example 3

Use Algebra to Find Missing Angle Measures

Combine like terms.

Add 20 to each side.

Simplify.

Divide each side by 5.

Simplify.

Example 3

Use Algebra to Find Missing Angle Measures

Step 2 Replace x with 22 to find the measure of

each angle.

m?DEF 2x m?WXY 3x 20 2(22)

or 44 3(22) 20 or 46

Answer m?DEF 44 and m?WXY 46

Example 3

Angles RST and ABC are complementary angles with

m?RST 3x and m?ABC x 10. What are the

measures of ?ABC and ?RST?

A. m?ABC 12 and m?RST 78 B. m?ABC 20 and

m?RST 70 C. m?ABC 30 and m?RST

60 D. m?ABC 30 and m?RST 70

End of the Lesson