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Unit 3 Review Packet 2 1. Find the sum of the measures of the angles of the figure. 2. ABCD is a parallelogram. If A then B D C 3. ABCD is a parallelogram. If A then The diagram is not to scale. B D ____ The diagram is not to scale. C 4. WXYZ is a parallelogram. Name an angle congruent to X Y N W A. Z B. C. D. 5. Find AM in the parallelogram if PN =12 and AO = 5. The diagram is not to scale. M N A P O 6. LMNO is a parallelogram. If NM = x + 34 and OL = 5x + 6, find the value of x and then find NM and OL. O N L M 7. If find A D so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. B C 8. If and be a parallelogram. The diagram is not to scale. O N L ____ M 9. Which statement is true? A. All parallelograms are rectangles. B. All quadrilaterals are parallelograms. C. All rectangles are squares. D. All parallelograms are quadrilaterals. find the values of x and y for which LMNO must 10. In rectangle KLMN, KM = and LN = 45.5. Find the value of x. K L N M 11. Find the values of a and b. The diagram is not to scale. a° 111° 68° b° 12. and Find The diagram is not to scale. R | | S || || U T 13. Find the measures of an interior angle and an exterior angle of a regular polygon with 8 sides. 14. What type of quadrilateral has all sides congruent? 15. Isosceles trapezoid ABCD has legs find the value of y. and and base If AB = 4y – 5, BC = 2y – 5, and CD = 5y – 17, 16. B is the midpoint of D is the midpoint of and AE = 21. Find BD. The diagram is not to scale. C B D A E 17. Identify parallel segments in the diagram. C 8 6 B D 8 6 A 5 F 5 E 18. Find the value of x. The diagram is not to scale. 72° 105° x° ____ 19. Which description does NOT guarantee that a quadrilateral is a parallelogram? A. a quadrilateral with consecutive angles supplementary B. quadrilateral with two opposite sides parallel C. a quadrilateral with the diagonals bisecting each other D. a quadrilateral with both pairs of opposite sides congruent 20. Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 5-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 4-gon, one at each vertex. What are | 1 The diagram is not to scale. | 21. In the rhombus, | | 3 2 22. Find the measure of the numbered angles in the rhombus. The diagram is not to scale. 33º 1 3 2 23. DEFG is a rectangle. DF = 6x – 2 and EG = x + 8. Find the value of x and the length of each diagonal. 24. What is the sum of the angle measures of a 24-gon? 25. In rectangle PQRS, PR = 20x – 20 and QS = x + 512. Find the value of x and the length of each diagonal. P Q S R 26. In quadrilateral ABCD, and A D B C . For what value of x is ABCD a rhombus? 27. In quadrilateral ABCD, and A . For what value of x is ABCD a rectangle? B E D C 28. The sum of the angle measures of a polygon with s sides is 3600. Find s. 29. Find in the kite. The diagram is not to scale. | 1 3 2 B || || D 29° | A C 30. What is the measure of one angle in a regular 20-gon? 31. In parallelogram DEFG, DH = x + 2, HF = 2y, GH = 2x – 2, and HE = 2y + 2. Find the values of x and y. The diagram is not to scale. D E H G F 32. A road sign is in the shape of a regular decagon. What is the measure of each angle on the sign? Round to the nearest tenth. 33. Find the missing values of the variables. The diagram is not to scale. 123° 127° x° y° 77° 34. Points B, D, and F are midpoints of the sides of The diagram is not to scale. EC = 30 and DF = 17. Find AC. A B F C D E 35. Find the value of x. 14 2x – 9 36. Find the value of x. The diagram is not to scale. 45 x 45 35 24 24 37. The sum of the measures of two exterior angles of a triangle is 257. What is the measure of the third exterior angle? 38. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 150 ft ( 39. Use the information in the diagram to determine the measure of the angle x formed by the line from the point on the ground to the top of the building and the side of the building. The diagram is not to scale. X ( 52º 40. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. A B 4x – 18 y + 13 4y – 5 x + 12 D C 41. How many sides does a regular polygon have if each exterior angle measures 30? 42. Find the value of x. The diagram is not to scale. 110° x° 57° 43. Find the measure of each interior and exterior angle. The diagram is not to scale. 5 4 115 o 6 1 2 9 8 7 3 44. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale. o 31 x w y v o 68 z 45. Find the values of x, y, and z. The diagram is not to scale. 46° 13° 58° x° z° y° 46. This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. x x 47. For the parallelogram, if and 3 find The diagram is not to scale. 4 2 1 48. Use less than, equal to, or greater than to complete this statement: The measure of each exterior angle of a regular 7-gon is ____ the measure of each exterior angle of a regular 4-gon. 49. Find the value of x. The diagram is not to scale. (3x + 10)º 148º (x)º 112º 50. Find the length of the midsegment. The diagram is not to scale. 47 56 4x + 2 56 47 4x + 44 Find the value of each variable. The diagram is | | 51. In the rhombus, not to scale. 3 1 | | 2 52. Which description does NOT guarantee that a trapezoid is isosceles? A. both pairs of base angles congruent B. congruent legs C. congruent bases D. congruent diagonals 53. A nonregular hexagon has five exterior angle measures of 51, 60, 68, 53, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle? 54. B is the midpoint of and D is the midpoint of Solve for x, given C B D A E 55. Find the values of the variables and the lengths of the sides of this kite. y–2 | x+ 2 || || | 2x + 3 x+ 6 56. Find the value of x. The diagram is not to scale. Given: , , S R T U and 57. Find the values of the variables in the parallelogram. The diagram is not to scale. 109 20 y° x° z° 58. For what values of x and y must this quadrilateral be a parallelogram? Find the lengths of the sides. The diagram is not to scale. 7x 2x + 2 4y 8y + 11 59. In the parallelogram, and J Find The diagram is not to scale. K O M L 60. In the parallelogram, and P Q O S R Find The diagram is not to scale. Unit 3 Review Packet 2 Answer Section 1. 2. 3. 4. 5. 6. 7. 900 119 100 C 5 x = 7, NM = 41, OL = 41 133 7 8. x = 10, y = 2 9. D 10. 3.5 11. 12. 20 13. m (interior) = 135 m (exterior) = 45 14. rhombus 15. 12 16. 10.5 17. 18. 33 19. B 20. equal to 21. 22. 23. x = 2, DF = 10, EG = 10 24. 3960 25. x = 28, PR = 540, QS = 540 26. 3 27. 14 28. 22 29. 30. 162 31. x = 6, y = 4 32. 144 33. x = 107, y = 53 34. 34 35. 8 36. 70 37. 103 38. 75 ft 39. 52 40. x = 10, y = 6 41. 12 sides 42. 13 43. 44. [4] [3] [2] [1] 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. Because the three interior angles of a triangle have measures with sum 180, w + 31 + 90 = 180, so w = 59. Because vertical angles are congruent, y = 59. Because supplementary angles have measures with sum 180, x = v = 121. Because the three interior angles of a triangle have measures with sum 180, z + 68 + y = z + 68 + 59 = 180, so z = 53. small error leading to one incorrect answer three correct answers, work shown two correct answers, work shown 36° 158 less than 45 42 x = 45, y = 45, z = 9 C 109 x = 3, y = 7; 5, 9 76 x = 5, y = 3; 12, 35 107 94