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1.5 –Describe Angle Pair Relationships

1.5 –Describe Angle Pair Relationships. Adjacent angles:. Two angles that share a common side and vertex. 2. 1. 1 is adjacent to 2. Complementary Angles:. Two angles that add to 90 °. 1. 2. 1. 2. m 1 + m 2 = 90 °. Supplementary Angles:. Two angles that add to 180 °. 2. 1. 1.

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1.5 –Describe Angle Pair Relationships

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  1. 1.5 –Describe Angle Pair Relationships

  2. Adjacent angles: Two angles that share a common side and vertex 2 1 1 is adjacent to 2

  3. Complementary Angles: Two angles that add to 90° 1 2 1 2 m1 + m2 = 90°

  4. Supplementary Angles: Two angles that add to 180° 2 1 1 m1 + m2 = 180° 2

  5. Two adjacent angles whose noncommon sides are opposite rays Linear Pair: 2 1 They will always add to 180° m1 + m2 = 180°

  6. Vertical Angles: Two angles whose sides form two pairs of opposite rays 1 2 They will always be congruent!

  7. 1. Tell whether the indicated angles are adjacent. EFG and HGF no

  8. 1. Tell whether the indicated angles are adjacent. JNM and MNK yes

  9. 2. Name a pair of complementary angles, supplementary angles, and vertical angles . Vertical: ROL and NOP L LOM and QOP M Complementary: R N QOR and ROL O MON and NOP Q P Supplementary: ROL and LON ROM and MON QOL and LOM

  10. 2. Name a pair of complementary angles, supplementary angles, and vertical angles . Vertical: DGE and BGC A EGB and DGC E Complementary: DGE and EGA G B D Supplementary: C DGE and EGB DGA and AGB EGA and AGC

  11. 3. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 90 – 82 = 8°

  12. 3. 1 and 2 are complementary angles. Given the measure of 1, find m2. m1 = 23° m2 = 90 – 23 = 67°

  13. 4. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 82° m2 = 180 – 82 = 98°

  14. 4. 1 and 2 are supplementary angles. Given the measure of 1, find m2. m1 = 105° m2 = 180 – 105 = 75°

  15. 5. Find the measure of ABD and DBC. 4x + 6 + 11x – 6 = 180 15x = 180 x = 12 4(12)+6 mABD = = 48+6 = 54° 11(12)-6 mDBC = = 132-6 = 126°

  16. 5. Find the measure of ABD and DBC. 2x + 3x = 90 5x = 90 x = 18 2(18) mABD = = 36° 3(18) mDBC = = 54°

  17. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 1 and 2 Linear pair

  18. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 1 and 3 Vertical angles

  19. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 2 and 4 Vertical angles

  20. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 5 and 7 neither

  21. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither. 5 and 8 neither

  22. 7. Find the values of x and y. 6x – 11 + 2x – 9 = 180 8x – 20 = 180 8x = 200 x = 25° 20y + 19 + 2x – 9 = 180 20y + 19 + 2(25) – 9 = 180 20y + 60 = 180 20y = 120 y = 6°

  23. 7. Find the values of x and y. 21x – 3 + 5x + 1 = 180 26x – 2 = 180 26x = 182 x = 7° 4y + 17y – 9 = 180 21y – 9 = 180 21y = 189 y = 9°

  24. HW Problem # 50 Vertical angles Ans: ex: AGB & EGD

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