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Petersonscom geometry 223 solutions to practice

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Unformatted text preview: cle the letter that appears before your answer. 1. The area of a trapezoid whose bases are 10 and 12 and whose altitude is 3 is (A) 66 (B) 11 (C) 33 (D) 25 1 (E) 16 2 6. In triangle ABC, the angles are in a ratio of 1 : 1 : 2. The largest angle of the triangle is (A) 45° (B) 60° (C) 90° (D) 120° (E) 100° Find the number of degrees in each angle of a regular pentagon. (A) 72 (B) 108 (C) 60 (D) 180 (E) 120 Find the number of degrees in arc AB. 2. The circumference of a circle whose area is 16π is (A) 8π (B) 4π (C) 16π (D) 8 (E) 16 Find the perimeter of a square whose diagonal is 8. (A) 32 (B) 16 (C) 32 2 (D) 16 2 (E) 32 3 The length of the line segment joining the point A(4, –3) to B(7, –7) is (A) (B) (C) (D) (E) 7 6 5 1 2 221 185 7. 3. 8. 4. (A) (B) (C) (D) (E) 9. 80 20 60 100 90 5. Find angle x if AB is parallel to CD . Find the edge, in inches, of a cube whose volume is equal to the volume of a rectangular solid 2 in. by 6 in. by 18 in. (A) 4 (B) 8 (C) 5 (D) 6 (E) 7 10. If the volume of one cube is 8 times as great as another, then the ratio of the area of a face of the larger cube to the area of a face of the smaller cube is (A) (B) (C) (D) (E) 35° 80° 245° 65° 55° (A) (B) (C) (D) (E) 2:1 4:1 2 :1 8:1 2 2 :1 www.petersons.com Geometry 223 SOLUTIONS TO PRACTICE EXERCISES Diagnostic Test 1. (A) Represent the angles as 5x, 6x, and 7x. They must add up to 180°. 18 x = 180 x = 10 6. (D) The remaining degrees of the triangle are 180 – x. Since the triangle is isosceles, the remaining angles are equal, each 180 − x x = 90 − . 2 2 The angles are 50°, 60°, and 70°, an acute triangle. 2. (B) The area of a circle is πr2. The area of a circle with radius x is πx2, which equals 4. The area of a circle with radius 3x is π (3x)2 = 9πx2 = 9 · 4 = 36. (D) 7. (D) 3. Angle ABX = 90° – 37° = 53° Angle ABY = 180° – 53° = 127° 8. (C) 22 + 32 = x 2 4 + 9 = x2 13 = x 2 13 = x 4. (E) 9. Extend FE to H. ∠EHG = ∠AFE = 40°. ∠HEG must equal 110° because there...
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