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Identify adjacent, vertical, complementary, and supplementary angles.

Objectives. Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles. Vocabulary. adjacent angles linear pair complementary angles supplementary angles vertical angles. Example 1: Identifying Angle Pairs.

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Identify adjacent, vertical, complementary, and supplementary angles.

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  1. Objectives Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles.

  2. Vocabulary adjacent angles linear pair complementary angles supplementary angles vertical angles

  3. Example 1: Identifying Angle Pairs Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. A. AEB and BED B. AEB and BEC C. DEC and AEB

  4. Example 1Continued Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. D. 5 and 6 E. 7 and SPU F. 7 and 8

  5. complement of an angle = supplement of an angle =

  6. Example 2: Finding the Measures of Complements and Supplements Find the measure of each of the following. A. complement of F B. supplement of G

  7. Example 3: Using Complements and Supplements to Solve Problems An angle is 10° more than 3 times the measure of its complement. Find the measure of the complement.

  8. 1 3 4 2 Four Steps to Problem-Solving:

  9. Example 4a: Light passing through a fiber optic cable reflects off the walls of the cable in such a way that 1 ≅ 2, 1 and 3 are complementary, and 2 and 4 are complementary. If m1 = 47°, find m2, m3, and m4.

  10. Example 4b: What if...?Suppose m3 = 27.6°. Find m1, m2, and m4.

  11. _________________= two nonadjacent angles formed by two intersecting lines. __________are vertical angles, as are __________.

  12. Example 4 Name the pairs of vertical angles.

  13. Example 6a: HML and JMK are supplementary angles. Find the measures of both angles.

  14. Example 6b: HMJ and LMK are complementary angles. Find the measures of both angles.

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