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Example 1

Example 1. Determine whether the labeled angles are vertical angles , a linear pair , or neither. SOLUTION. Identify Vertical Angles and Linear Pairs. b. c. a. a. 1 and  2 are a linear pair because they are adjacent and their noncommon sides are on the same line. b.

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Example 1

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  1. Example 1 Determine whether the labeled angles are vertical angles, a linear pair,or neither. SOLUTION Identify Vertical Angles and Linear Pairs b. c. a. 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6are vertical angles because they are not adjacent and their sides are formed by two intersecting lines.

  2. Example 2 Find the measure of RSU. SOLUTION RSU andUST are a linear pair. By the Linear Pair Postulate, they are supplementary. To findmRSU,subtract mUST from180°. mRSU =180°– mUST = 180°–62° = 118° Use the Linear Pair Postulate

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

  4. Example 4 Findm1, m2,andm3. SOLUTION Find Angle Measures m2 = 35° Vertical Angles Theorem m1 = 180° – 35° = 145° LinearPairPostulate m3 = m1= 145° Vertical Angles Theorem

  5. Checkpoint Findm1, m2,andm3. Find Angle Measures 1. m1 = 152°; m2 = 28°;m3 = 152° ANSWER 2. m1 = 56°; m2 = 124°;m3 = 56° ANSWER 3. m1 = 113°; m2 = 67°;m3 = 113° ANSWER

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