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Chap 2 Sec 4 Vertical Angles and Linear Pairs When 2 lines intersect we see 4 individual angles formed 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.

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

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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.

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

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

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Example 4 Find Angle Measures Find m 1, m 2, and m 3. SOLUTION m 2 = 35° Vertical Angles Theorem m 1 = 180° – 35° = 145° Linear Pair Postulate m 3 = m 1 = 145° Vertical Angles Theorem

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Checkpoint Find Angle Measures ANSWER m 1 = 152° ; m 2 = 28° ; m 3 = 152° ANSWER m 1 = 56° ; m 2 = 124° ; m 3 = 56° ANSWER m 1 = 113° ; m 2 = 67° ; m 3 = 113° Find m 1, m 2, and m

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Example 5 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 –2 –2y–2y = Divide each side by –2. 21 = y Simplify.

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

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