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**When 2 lines intersect we see 4 individual angles formed.**

Chap 2 Sec 4 Vertical Angles and Linear Pairs When 2 lines intersect we see 4 individual angles formed. 1 2 3 4 We usually talk about these angles 2 at a time. The term we use depends on which 2 angles we are talking about. If the 2 angles are across from each other (not adjacent), then they are called vertical angles. If the 2 angles are beside each other (adjacent), then they are called a linear pair. 1

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**Vertical angles are congruent.**

Chap 2 Sec 4 Vertical Angles and Linear Pairs 1 2 3 4 Recognizing these angle pairs is important because they have special relationships. Vertical angles are congruent. Linear pairs are supplementary (180°). 2

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**Determine whether the labeled angles are vertical angles, **

Example 1 Identify Vertical Angles and Linear Pairs Determine whether the labeled angles are vertical angles, a linear pair, or neither. b. a. c. SOLUTION a. 1 and 2 are a linear pair because they are adjacent and their noncommon sides are on the same line. b. 3 and 4 are neither vertical angles nor a linear pair. c. 5 and 6 are vertical angles because they are not adjacent and their sides are formed by two intersecting lines. 3

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**Find the measure of RSU.**

Example 2 Use the Linear Pair Postulate Find the measure of RSU. SOLUTION RSU and UST are a linear pair. By the Linear Pair Postulate, they are supplementary. To find mRSU, subtract mUST from 180°. mRSU = 180° – mUST = 180° – 62° = 118° 4

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**Find the measure of CED.**

Example 3 Use the Vertical Angles Theorem Find the measure of CED. SOLUTION AEB and CED are vertical angles. By the Vertical Angles Theorem, CED AEB, so mCED = mAEB = 50°. 5

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**Example 4 Find m1, m2, and m3. SOLUTION m2 = 35°**

Find Angle Measures Find m1, m2, and m3. SOLUTION m2 = 35° Vertical Angles Theorem m1 = 180° – 35° = 145° Linear Pair Postulate m3 = m1 = 145° Vertical Angles Theorem 6

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**Checkpoint Find m1, m2, and m3. 1.**

Find Angle Measures Find m1, m2, and m3. 1. ANSWER m1 = 152°; m2 = 28°; m3 = 152° 2. ANSWER m1 = 56°; m2 = 124°; m3 = 56° 3. ANSWER m1 = 113°; m2 = 67°; m3 = 113°

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**Example 5 Find the value of y. SOLUTION**

Use Algebra with Vertical Angles Find the value of y. SOLUTION Because the two expressions are measures of vertical angles, you can write the following equation. (4y – 42)° = 2y° Vertical Angles Theorem 4y – 42 – 4y = 2y – 4y Subtract 4y from each side. –42 = –2y Simplify. –2 –42 –2y = Divide each side by –2. 21 = y Simplify. 8

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**Find the value of the variable.**

Checkpoint Use Algebra with Angle Measures Find the value of the variable. 4. ANSWER 43 5. ANSWER 16 6. ANSWER 5

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