College Math Placement Test Geometry 5 — Questions and Answers
Question 1: Two supplementary angles are in the ratio 2:7. What is the measure of the larger angle?
- 140° (Correct answer)
- 40°
- 126°
- 70°
Correct answer: 140°
2x + 7x = 180° → 9x = 180° → x = 20°; larger angle = 7(20°) = 140°.
Question 2: A square is inscribed in a circle of radius 5. What is the area of the square?
- 50 (Correct answer)
- 25
- 100
- 25π
Correct answer: 50
The diagonal of the square equals the diameter = 10; side = 10/√2 = 5√2; area = (5√2)² = 50.
Question 3: What is the slope of a line perpendicular to the line passing through (1, 3) and (4, 9)?
- −1/2 (Correct answer)
- 2
- 1/2
- −2
Correct answer: −1/2
Slope of given line = (9−3)/(4−1) = 2; perpendicular slope = −1/2.
Question 4: A triangle has vertices at (0,0), (6,0), and (0,8). What is its area?
- 24 (Correct answer)
- 48
- 12
- 30
Correct answer: 24
Area = ½ × base × height = ½ × 6 × 8 = 24.
Question 5: The diagonal of a square is 12√2. What is the perimeter of the square?
- 48 (Correct answer)
- 24
- 144
- 72
Correct answer: 48
Side = diagonal/√2 = 12√2/√2 = 12; perimeter = 4 × 12 = 48.
Question 6: An equilateral triangle has a perimeter of 30. What is its area?
- 25√3 (Correct answer)
- 150
- 75√3/2
- 50√3
Correct answer: 25√3
Side = 10; area = (√3/4)s² = (√3/4)(100) = 25√3.
Question 7: A rectangular garden is 12 m long and 9 m wide. A path of uniform width 1.5 m surrounds it on the outside. What is the area of the path?
- 72 m² (Correct answer)
- 108 m²
- 180 m²
- 63 m²
Correct answer: 72 m²
Outer dimensions: (12+3) × (9+3) = 15 × 12 = 180 m²; inner = 108 m²; path area = 180 − 108 = 72 m².
College Math Placement Test Geometry 5
Two supplementary angles are in the ratio 2:7.
What is the measure of the larger angle?