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Exploring Angle Relationships for Geometry Students

Identify adjacent, vertical, complementary, and supplementary angles. Find measures of angle pairs. Learn to solve problems using complements and supplements. A comprehensive guide with examples and vocabulary. Enhance your geometry skills!

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Exploring Angle Relationships for Geometry Students

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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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