2. Geometry 8 th Grade Algebraic Angles

3. Essential Questions How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?

5. How can I remember which angle is which? complementary or supplementary?

6. angles that add up to 90 º Review Complementary Angles–

7. angles that add up to 180 º Review Supplementary Angles –

8. 20 + x = 90 -20 - 20 x = 70 Complementary Supplementary 115 + x = 180 -115 - 115 x = 65

9. Linear Pair Two adjacent angles that form a line. They are supplementary. (angle sum = 180  ) 12 4 t 3  1+  2=180  2+  4=180  4+  3=180  3+  1=180

10. Supplementary Angles/ Linear Pair Find the measures of the missing angles ? 72  ? t 108  180 - 72

11. Who uses this stuff?

12. Congruent Angles – Angles with equal measurement  A ≅  B denotes that  A is congruent to  B.

13. Adjacent Angles - angles that share a common vertex and ray…angles that are back to back. *Vertex – the “corner” of the angle *Ray – a line that has an endpoint on one end and goes on forever in the other direction.

14. Vertical Angles Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles. 12 3 4 t 1   41   4  2   3

15. Vertical Angles Hint: V and A are facing opposite directions and are the same shape. Vertical Angles are facing opposite each other and are the same measurement.

16. Vertical Angles Find the measures of the missing angles 125  ? ? 55  t 125 

17. Review: Determine if the given angles are complementary, supplementary, vertical, or adjacent. 1) g and f 2) b, c, and d 3) f and e 4) a and d complementary supplementary adjacent vertical

18. 30° 55°125° 55°

19. 5x + 10 = 110 -10 -10 5x = 100 ÷5 ÷5 x = 20 Solve for x and find the algebraic angle.

20. Name the types of angles and solve for the algebraic angle...also known as a linear pair.

21. Write an equation and solve for both angles. x 3x + 10 x + 3x + 10 = 90 4x + 10 = 90 - 10 -10 4x = 80 4 x = 20 3x + 10 3(20) + 10 70

22. Write an equation and solve for both angles. x2x - 30 x + (2x - 30) = 180 3x - 30 = 180 +30 3x = 210 x = 70 70 2(70) – 30 = 110

23. x + 38 = 90 x = 52 Write an equation to solve for x.

24. Write an equation to solve for x and find the algebraic angle. 5x + 110 = 180 x = 14 5(14) = 70 º 5x º 110 º

25. Write an equation to solve for x and then find the two angle measurements. xºxº 4x º 4x + x = 180 5x = 180 x = 36 º 4(36) = 144 º

26. Solve for x. 83 º (2x + 1) º 2x + 1 = 83 x = 41

27. Solve for x and then find the angle measurements. 2x º (5x -108) º 2x = 5x – 108 108 = 3x 36 = x 2(36) = 72 º 5(36) – 108 = 72º

28. Solve for x. ___________ Solve for angle F.___________ 2x º 12 º Solve for x _______ Solve for the missing angle ____ Write equations to find the missing angles. 7x + 6 = 90 x = 12 7(12) + 6 = 90° 2x + 12 = 90 x = 39 78°

29. Exit Slip Explain how you find angle measures using Algebra.

30. Triangles

31. 180 Rule for Triangles - the sum of the interior angles of any triangle is always 180. a b c 40 80 x 40 + 80 + x = 180 120 + x = 180 x = 60

32. Find each angle below. y+14 y - 20 2y - 10 (y + 14) + (2y - 10) + (y - 20) = 180 4y - 16 = 180 +16 4y = 196 y = 49 y + 14 = 63 2y - 10 = 88 y - 20 = 29 180

33. Find the missing angle. 40132 x 48° 92°

34. Find the missing angle. 119 x 124 56° 61° 63°

35. 1. 2. 3. 4. Write and solve equations to find the angles below. x° z° 5 + x + 117 = 180° x = 58 5 + 58 = 63° 2x + 8 + 3x + 2 = 90° x = 16 2(16) + 8 = 40° 3(16) + 2 = 50° 145 + z = 180° z = 35° 110 + x = 180° x = 70° 35 + 70 + y = 180° y = 75° 3x + x + 20 + 2x + 10 = 90° x = 10 3(10) = 30° (10) + 20 = 30° 2(10) + 10 = 30°

36. Find e. e = 25° because vertical angles are equal. Sometimes it is easier than you first think to solve for the missing angle.

37. 113° 41° 101° n° Solve for n. 67° 79° 34° 105°

38. One angle in a pair of vertical angles is (4t + 16) º and the other angle is (5t – 21) º. 1) Vertical angles are ___________. 2) Write the equation that you will use to find the angle measurements.___________ 3) t = _________ 4) The two angle measurements are _____ and _______. congruent 5t – 21 = 4t + 16 37 º 164 º

39. 1.Find the measures of the angles labeled A, B, and C. 2. Find the measures of the angles labeled a, b, c, and d. 47° 72° 61° 55° 65° 30° 60°

40. In a linear pair of angles, one angle is three times larger than the other angle. 1)Linear pair angles are _______________. 2)The equation I will use to solve for the angle measurements is _____________. 3)X = ____________ 4)The angle measurements are ______ and _______. supplementary x + 3x = 180 45 º 135 º

41. Closing Write an equation to solve for x and then find the missing angle measurement. x = 10 5(10) + 2 = 52° x = 21 5(21) = 105°