Regents Geometry 3 — Questions and Answers
Question 1: In a circle, a central angle measures 80°. What is the measure of the arc it intercepts?
- 40°
- 160°
- 80° (Correct answer)
- 100°
Correct answer: 80°
A central angle equals the measure of its intercepted arc, so the arc is 80°.
Question 2: What is the volume of a rectangular prism with length 5 m, width 3 m, and height 4 m?
- 47 m³
- 60 m³ (Correct answer)
- 94 m³
- 120 m³
Correct answer: 60 m³
Volume = l × w × h = 5 × 3 × 4 = 60 m³.
Question 3: Two secants are drawn from an external point. The external segment of the first secant is 4 and its whole length is 9. The external segment of the second secant is 3. What is the whole length of the second secant?
- 10
- 12 (Correct answer)
- 8
- 6
Correct answer: 12
Secant-secant theorem: 4 × 9 = 3 × x, so x = 12.
Question 4: Which transformation preserves both shape and size (is an isometry)?
- Dilation
- Reflection (Correct answer)
- Horizontal stretch
- Shear
Correct answer: Reflection
Reflection is a rigid motion that preserves all distances and angles.
Question 5: A trapezoid has bases of 8 cm and 14 cm and a height of 5 cm. What is its area?
- 55 cm² (Correct answer)
- 110 cm²
- 56 cm²
- 112 cm²
Correct answer: 55 cm²
Area = ½ × (8 + 14) × 5 = 55 cm².
Question 6: In triangle ABC, angle A = 45° and angle B = 75°. What is the measure of angle C?
- 70°
- 60° (Correct answer)
- 40°
- 80°
Correct answer: 60°
Angle C = 180° − 45° − 75° = 60°.
Question 7: The diagonal of a square is 10 cm. What is the side length of the square?
- 5 cm
- 5√2 cm (Correct answer)
- 10√2 cm
- √10 cm
Correct answer: 5√2 cm
For a square, diagonal = s√2, so s = 10 ÷ √2 = 5√2 cm.
Regents Geometry 3
In a circle, a central angle measures 80°.
What is the measure of the arc it intercepts?