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01/23/17 Warm Up 2.4 On Desk Do the Daily Quiz 2.3

This lesson teaches how to calculate angle measures of vertical angles formed by intersecting lines. It also covers the concept of linear pairs and provides examples and practice problems.

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01/23/17 Warm Up 2.4 On Desk Do the Daily Quiz 2.3

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  1. 01/23/17Warm Up 2.4 On DeskDo the Daily Quiz 2.3

  2. ESSENTIAL OBJECTIVE Calculate Angle Measures of Angles formed by Intersecting Lines

  3. Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other. VOCABULARY

  4. Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

  5. Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

  6. Linear Pair: Two adjacent angles whose opposite rays form a straight line.

  7. Linear Pair: Two adjacent angles whose opposite rays form a straight line.

  8. 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. b. 3 and4 are neither. 5 and6are vertical angles c.

  9. Linear Pair Postulate: If two angles form a linear pair, then they are supplementary

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

  11. Vertical Angles Theorem Vertical Angles are Congruent (  )

  12. Vertical Angles Theorem Vertical Angles are Congruent (  )

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

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

  15. 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

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

  17. Example 5 SOLUTION Algebraic expressions are measures of vertical angles, you can write the following equation. –2y = –2 Use Algebra with Vertical Angles Find the value of y. (4y– 42)° = 2y° 4y– 42 – 4y= 2y – 4y –42 = –2y –42 21 = y –2 .

  18. Review

  19. Determine whether the angles are complementary, supplementary, or neither. Also tell whether the angles are adjacent or nonadjacent. 1. 2.

  20. Determine whether the angles are complementary, supplementary, or neither. Also tell whether the angles are adjacent or nonadjacent. 1. ANSWER complementary; adjacent 2. ANSWER neither; nonadjacent

  21. 3. mR = 27° 4. mT = 11° 5. In the figure at the right, ABDand DBC are complementary angles. Find the value of x. Find the measures of a complement and a supplement of the angle.

  22. 3. mR = 27° 63°; 153° ANSWER 4. mT = 11° 79°; 169° ANSWER 5. In the figure at the right, ABDand DBC are complementary angles. Find the value of x. ANSWER x = 7 Find the measures of a complement and a supplement of the angle.

  23. Hw Worksheet 2.4 B

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