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1 Acc. Geometery Name Polygon Review Per/Sec. Date Determine whether each of the following statements is always, sometimes, or never true. 1. A regular polygon is convex. 2. Two sides of a polygon are noncollinear. 3. An equilateral polygon is regular. 4. A pentagon has a right angle. 5. A trapezoid is a quadrilateral. 6. A trapezoids has a right angle. 7. The opposite angles of an isosceles trapezoid are supplementary. 8. A regular quadrilateral is a square. 9. The sum of the measures of the exterior angles of a convex polygon is An equiangular polygon is a regular polygon An equiangular triangle is a regular triangle As the number of sides of a convex polygon increases, the sum of the interior angles increases In an equiangular polygon with more than 4 sides, an interior angle is greater than an exterior angle In a convex polygon with more than 4 sides, an interior angle is greater than an exterior angle The measures of three of the angles of a quadrilateral equal 1 20, 75, and 80. Find the degree measure of the fourth angle Classify the given polygon. a) 80 d) 1 00 b) 85 e) 1 05 c) 90 a) quadrilateral b) pentagon c) heptagon d) octagon e) decagon

2 Page How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) The sum of the measures of a polygon is What kind of polygon is it? a) hexagon b) heptagon c) octagon d) decagon e) dodecagon 20. If 4 XYZ is a right isosceles triangle, find the measure of the three angles of the triangle. a) 30, 30, 90 b) 30, 60, 90 c) 40, 50, 90 d) 45, 45, 90 e) 60, 60, Two angles of a triangle measure 1 8 and 77. Find the measure of the third angle. 22. In the given figure, m 6 X = 47 and m 6 W = 92, find m 6 WYZ. a) 1 9 b) 36 c) 59 d) 64 e) 85 a) 88 b) 1 00 c) 1 33 d) 1 39 e) In the given diagram, if m 6 B = and m 6 A = 1 5, find the degree measure of the exterior 6 BCD. 24. Which of the following is true about the figure? a) 53 b) 68 c) 1 27 d) 1 65 e) 1 80 a) b = e b) a + b = d + e c) a + b = 2(d + e) d) a + b 42 = d + e e) a + b + d + e = 1 80

3 Page Find the sum of the degree measures of all the exterior angles of a hexagon. a) 36 b) 72 c) 90 d) 1 80 e) Classify the given polygon. a) pentagon b) octagon c) quadrilateral d) hexagon e) decagon 27. Find the sum of the degree measures of all the interior angles of a hexagon. a) 540 d) b) 720 e) c) Name the regular polygon with interior angles which each measure a) triangle b) pentagon c) hexagon d) octagon e) decagon 29. Which of the following figures are polygons? I. 30. How many diagonals can be drawn in a convex polygon with 1 1 sides? a) 36 b) 39 c) 40 d) 44 e) 46 II. III. a) I only b) III only c) I and II only d) I and III only e) II and III only 31. Which of the following polygons is a quadrilateral? a) square b) pentagon c) hexagon d) triangle e) octagon 32. The sum of the measures of the interior angles of a quadrilateral is degrees. a) 270 b) 360 c) 540 d) 720 e) 1 080

4 Page The measures of three of the angles of a quadrilateral equal 80, 50, and 90. Find the degree measure of the fourth angle. 34. What is the name of a polygon having 4 sides? a) 50 d) 1 20 b) 80 e) 1 40 c) What is the name of a polygon having 1 0 sides? 36. What is the name of a polygon having 1 2 sides? 37. How many sides does a regular polygon have if its perimeter is 65 cm and each side length is 1 3 cm? 38. In the diagram, polygon ABCDEFGHI is regular and HG = 4. What is the perimeter of this polygon? 39. What is the sum of the measures of the interior angles of a convex heptagon? 40. What is the measure of one interior angle of a regular octagon? 41. What convex polygon has an interior angle sum of 720? 42. Find the number of sides of a regular polygon with an interior angle measuring 60 degrees.

5 Page Find the number of sides of a regular polygon with an interior angle measuring 1 78 degrees. 44. Find the total number of diagonals in a convex n -gon. 45. The number of sides of a polygon is increased by n, increasing the sum of the measures of the interior angles of the polygon by 720. Find n. 46. In a convex polygon, the sum of all the interior angles except one is What is the least number of sides this polygon can have? 47. The sum of the measures of seven angles of a convex decagon is Of the remaining three angles, precisely two are complementary and precisely two are supplementary. What is the measure of these three angles? 48. Use the diagram to determine these values: a b c d e f g h 49. An equiangular polygon has 1 8 sides. What is the measure of one exterior angle of this polygon? 50. A regular polygon has an exterior angle of 1 5. How many sides does this polygon have?

6 Page What equiangular polygon has an exterior angle measure of ? 52. A quadrilateral has 3 exterior angles measuring 60, 80, and 70. What is the measure of the other exterior angle? 53. Solve for a. 54. In the diagram, points D and E are midpoints of sides AB and AC, respectively. If m 6 C = 65, what is the measure of 6 AED? 55. In the diagram, m 6 A = x 6, m 6 B = x + 4, and m 6 BCD = is the measure of 6 B? What

7 Acces format version 3.60B c EducAide Software Licensed for use by Lemont Township High School Acc. Geometery Polygon Review 2/1 4/2005 Answer List 1. Always 2. Sometimes 3. Sometimes 4. Sometimes 5. Always 6. Sometimes 7. Always 8. Always 9. Always 1 0. Sometimes 1 1. Always 1 2. Always 1 3. Always 1 4. Sometimes 1 5. b 1 6. c 1 7. d 1 8. e 1 9. d 20. d 21. e 22. d 23. c 24. b 25. e 26. e 27. b 28. c 29. b 30. d 31. a 32. b 33. e 34. quadrilateral 35. decagon 36. dodecagon units gon hexagon 42. triangle n(n 3) , 50, 1 30 (in any order) 48. a = 65, b = 57: 5, c = 80: 5, d = 32: 5, e = 1 1 9: 5, f = 27: 5, g = 1 32: 5, h = 85: gon Catalog List 1. GEO DC 3 2. GEO DC 5 3. GEO DC 7 4. GEO DC 9 5. GEO DC GEO DC GEO DC GEO DC GEO DC GEO DC GEO DC GEO DC GEO DC GEO DC MMA MA MMA MA MMA MA MMA MA MMA MA MMA LA MMA LA MMA LA MMA LA MMA LA MMA MA MMA MA MMA MA MMA MA MMA MA MMA MA MMA MA MMA MA MMA MA GEO DA GEO DA GEO DA GEO DG GEO DG GEO DH GEO DH GEO DH GEO DH GEO DH GEO DH GEO DH GEO DH GEO DH GEO DH GEO DI GEO DI GEO DI GEO DI GEO DI GEO EE GEO ED 51

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