I CAN use theorems to determine the relationships between specific pairs of angles and use algebra to find angle measures.

Learning Target

Use Corresponding Angles Postulate

A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.

Answer: m15 = 51

15 11 Corresponding Angles Postulate

m15 = m11 Definition of congruent angles

m15 = 51 Substitution

Use Corresponding Angles Postulate

B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.

Answer: m16 = 51

15 11 Corresponding Angles Postulate

15 16 Substitution

11 16 Supplement Theorem

m11 = m16 Definition of Congruent Angles

m16 = 51 Substitution

A. A

B. B

C. C

D. D

A. 42

B. 84

C. 48

D. 138

A. In the figure, a || b and m18 = 42. Find m22.

A. A

B. B

C. C

D. D

A. 42

B. 84

C. 48

D. 138

B. In the figure, a || b and m18 = 42. Find m25.

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Use Theorems about Parallel Lines

FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.

2 3 Alternate Interior Angles Postulate

m2 = m3 Definition of congruent angles

125 = m3 Substitution

Answer: m3 = 125

A. A

B. B

C. C

D. D

A. 25

B. 55

C. 70

D. 125

FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.

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A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.

Find Values of Variables

5 7 Corresponding Angles Postulate

m5 = m7 Definition of congruent angles

2x – 10 = x + 15 Substitution

x – 10 = 15 Subtract x from each side.

x = 25 Add 10 to each side.

Answer: x = 25

B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.

Find Values of Variables

8 6 Corresponding AnglesPostulate

m8 = m6 Definition of congruentangles

4y = m6 Substitution

Find Values of Variables

m6 + m4 = 180 Supplement Theorem

4y + 4(y – 25) = 180 Substitution

4y + 4y – 100 = 180 Distributive Property

8y = 280 Add 100 to each side.

y = 35 Divide each side by 8.

Answer: y = 35

A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.

A. A

B. B

C. C

D. D

A. x = 9

B. x = 12

C. x = 10

D. x = 14

B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.

A. A

B. B

C. C

D. D

A. y = 14

B. y = 20

C. y = 16

D. y = 24

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