1. Angles and Angle Pairs

2. Angle Definition Angle- is the union of two noncollinear rays that have a common endpoint.

3. Name that Angle!!! D O G D O G D O G D O G D O G D O G D O G D O G D O G D O G D O G 4

4. What if we added ray OC Is ∠O still ∠DOG ? C D O G D O G D O G D O G D O G D O G D O G D O G D O G D O G O G ∠O is nada because: ∠COD ∠DOC ∠DOG ∠GOD ∠COG ∠GOC

5. Classifying Angles

6. Complementary Angles 60° 30° Two angles that add up to 90° X 25° What is X? X + 25 = 90 -25 -25 X = 65

7. Supplementary Angles 120° 60° Two angles that add up to 180° N 130° x M G A m∠MAN + m∠NAG = 180 130 + X = 180 -130 = -130 X = 50

8. Adjacent Angles H G A M R F I ∠HAG and ∠MAG are adjacent angles because: Share a common side Share a common vertex Are ∠RIG and ∠FIT adjacent angles? NO! Common vertex , Yes Common side, No G T

9. Linear Pair 120° 60° Adjacent Angles that are Supplementary Is this a linear pair? N NO M G A m∠MAN + m∠NAG = 180

10. Are all linear pairs supplementary? YES Are all supplementary angles linear pairs? NO 40° 140°

11. 1 4 3 2 Vertical Angles <1 and <2 are vertical angles <3 and <4 are vertical angles Vertical Angles are Congruent

12. t m n Linear Pairs Congruent or Supplementary ? 4x + 5x = 180 9x = 180 9x = 180 9 9 4x 5x x = 20 4x 5x 4(20) 5(20) 100 80 80 100

13. t m n Practice #1 Congruent or Supplementary ? 3x + 6x = 180 9x = 180 9x = 180 9 9 3x 6x x = 20 3x 6x 3(20) 6(20) 120 60 120 60

14. t m n Vertical angles Congruent or Supplementary ? 3x + 20 = 7x - 8 -3x -3x 20 = 4x - 8 +8 +8 28 = 4x 4 4 3x + 20 7 = x 7x - 8 3x + 20 7x - 8 3(7) + 20 7(7) - 8 41 41 41 41

15. t m n Practice #2 Congruent or Supplementary ? 3x + 40 = 2x + 70 -2x -2x x + 40 = 70 2x + 70 -40 = -40 x = 30 3x + 40 3x + 40 2x + 70 3(30) + 40 2(30) + 70 130 130 130 130

16. Summary 3x+10 CONGRUENT ANGLES - SET THEM EQUAL 3x + 10 = x - 6 x - 6 SUPPLEMENTARY ANGLES -ADD TOGETHER and SET EQUAL to 180 6x + 3x = 180 6x 3x