1. Using the figure on the right, classify the relationship between <1 and <4

2. Using the figure on the right, find the measure of each angle.

m<9 = 2x – 4

m<10 = 2x +4

PROBLEMS OF THE DAY/HOMEWORK QUIZ!

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You named angle pairs formed by parallel lines and transversals.

• Use theorems to determine the relationships between specific pairs of angles.

• Use algebra to find angle measurements.

3.2 Angles and Parallel Lines

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 Theorem

m2 = m3 Definition of congruent angles

125 = m3 Substitution

Answer: m3 = 125

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

• In summary,

When you have parallel lines and a transversal, you will have

-Congruent corresponding angles

-Congruent alternate interior angles

-Congruent alternate exterior angles

-Supplementary consecutive angles

-Congruent vertical angles **These are always congruent

You can use these “facts” to solve for unknown angles and values of x!