1. Question 1: Find the measure of A. A B C 145° 44°

2. Question 1: SOLUTION The measure of an exterior angle is the sum of the two remote interior angles. A B C 145° 44° 101

3. Question 2: Find DC if HL = 68. H D S C L

4. Question 2: SOLUTION By the Midline Theorem, DC is half the length of HL. H D S C L DC = 34

5. Question 3: Find the sum of the exterior angles in a regular dodecagon.

6. Question 3 SOLUTION: The sum of the exterior angles in any polygon is always 360°. 360°

7. Question 4: Find the sum of the angles in a 62-gon.

8. Question 4 SOLUTION: Find the sum of the angles in a 62-gon. 10800°

9. Question 5: Find the number of diagonals that can be drawn in a regular octagon.

10. Question 5 SOLUTION: Find the number of diagonals that can be drawn in a regular octagon. 20

11. Question 6: How many sides does a pentadecagon have?

12. Question 6 SOLUTION: A pentadecagon has 15 sides. 15

13. Question 7: Find the number of sides in a regular polygon whose exterior angles each measure 7.5°.

14. Question 7 SOLUTION: Find the number of sides in a regular polygon whose exterior angles each measure 7.5°. 48

15. Question 8: Solve x 2 + 5x = 84 by factoring. What is the greater of the two solutions?

16. Question 8 SOLUTION: Solve x 2 + 5x = 84 by factoring. What is the greater of the two solutions? x 2 + 5x – 84 = 0 (x - 7)(x + 12) = 0 x - 7 = 0 x = 7 x + 12 = 0 x = -12 7

17. Question 9: The sum of the interior angles of a polygon is 7740°. How many sides does the polygon have?

18. Question 9 SOLUTION: The sum of the interior angles of a polygon is 7740°. How many sides does the polygon have? 45

19. Question 10: Find the measure of an interior angle in a regular decagon.

20. Question 10 SOLUTION: Find the measure of an interior angle in a regular decagon. 144

21. Question 11: A polygon has 54 diagonals. How many sides does the polygon have?

22. Question 11 SOLUTION: A polygon has 54 diagonals. How many sides does the polygon have? 12

23. Question 12: What is the measure of an exterior angle in a regular 72-gon?

24. Question 12 SOLUTION: What is the measure of an exterior angle in a regular 72-gon? 5

25. Question 13: The measure of an angle in a regular polygon is 140°. How many sides does the polygon have?

26. Question 13 SOLUTION: The measure of an angle in a regular polygon is 140°. How many sides does the polygon have? 9

27. Question 14: Find the measure of the missing angle in the triangle. 36°

28. Question 14 SOLUTION: Find the measure of the missing angle in the triangle. 36° 54 180 – 90 – 36 = 54°

29. Question 15: The ratio of an interior angle to an exterior angle in a regular polygon is 7:1. How many sides does the polygon have?

30. Question 15 SOLUTION: The ratio of an interior angle to an exterior angle in a regular polygon is 7:1. How many sides does the polygon have? 16 Interior and exterior angles are supplementary. 1x + 7x = 180 8x = 180 x = 22.5 Exterior angle = 22.5°

31. Question 16: Find the measure of S. H D S C L 67° 82°

32. Question 16 SOLUTION: Find the measure of S. 31 H D S C L 67° 82° 67° 82° 180 – 82 – 67 = 31°

33. Question 17: Solve for x. (x + 2)° (2x - 18)° (4x-11)°(2x + 8)° (3x + 7)°

34. Question 17 SOLUTION: Solve for x. (x + 2)° (2x - 18)° (4x-11)° (2x + 8)° (3x + 7)° 46 (x+2)+(2x-18)+(4x-11)+(2x+8)+(3x+7)=540 12x – 12 = 540 12x = 552 x = 46

35. Question 18: Find the number of diagonals in a 16-gon.

36. Question 18 SOLUTION: Find the number of diagonals in a 16-gon. 104

37. Question 19: Solve x 2 – 13x + 42 = 0 by factoring. Then find the smaller of the two solutions.

38. Question 19 SOLUTION: Solve x 2 – 13x + 42 = 0 by factoring. Then find the smaller of the two solutions. 6 x 2 – 13x + 42 = 0 (x – 7)(x – 6) = 0 x – 7 = 0 x = 7 x – 6 = 0 x = 6

39. Question 20: Find the measure of an angle in a regular 18-gon.

40. Question 20 SOLUTION: Find the measure of an angle in a regular 18-gon. 160

41. Question 21: The vertex angle in an isosceles triangle measures 62°. Find the measure of one base angle.

42. Question 21 SOLUTION: The vertex angle in an isosceles triangle measures 62°. Find the measure of one base angle. 59 62° x°x° x°x° x + x + 62 = 180 2x + 62 = 180 2x = 118 x = 59

43. Question 22: The measure of an exterior angle of a regular polygon is 15°. Find the number of sides in the polygon.

44. Question 22 SOLUTION: The measure of an exterior angle of a regular polygon is 15°. Find the number of sides in the polygon. 24

45. Question 23: How many sides does a polygon have if it has 275 diagonals?

46. Question 23 SOLUTION: How many sides does a polygon have if it has 275 diagonals? 25

47. The End!