Regents Geometry 4 — Questions and Answers
Question 1: An inscribed angle in a circle intercepts an arc of 140°. What is the measure of the inscribed angle?
- 140°
- 70° (Correct answer)
- 280°
- 40°
Correct answer: 70°
An inscribed angle equals half its intercepted arc: 140° ÷ 2 = 70°.
Question 2: Line segment AB has endpoints A(−3, 4) and B(5, −2). What is the length of AB?
- 10 (Correct answer)
- √28
- √128
- 14
Correct answer: 10
AB = √((5−(−3))² + (−2−4)²) = √(64 + 36) = √100 = 10.
Question 3: A cylinder has radius 3 in and height 10 in. What is its lateral surface area? (Use π ≈ 3.14)
- 94.2 in²
- 188.4 in² (Correct answer)
- 282.6 in²
- 28.26 in²
Correct answer: 188.4 in²
Lateral SA = 2πrh = 2 × 3.14 × 3 × 10 = 188.4 in².
Question 4: A translation moves point (−1, 4) to (3, 1). What is the translation vector?
- (4, −3) (Correct answer)
- (−4, 3)
- (2, 5)
- (−2, −5)
Correct answer: (4, −3)
Translation vector = (3−(−1), 1−4) = (4, −3).
Question 5: Two triangles are congruent by SAS. Which parts must be known to be congruent?
- Three sides
- Two sides and the included angle (Correct answer)
- Two angles and a side
- All three angles
Correct answer: Two sides and the included angle
SAS requires two pairs of congruent sides and the included angle between them.
Question 6: What is the equation of a circle centered at (3, −2) with radius 5?
- (x+3)² + (y−2)² = 25
- (x−3)² + (y+2)² = 25 (Correct answer)
- (x−3)² + (y+2)² = 5
- (x+3)² + (y−2)² = 5
Correct answer: (x−3)² + (y+2)² = 25
Standard form (x−h)² + (y−k)² = r² gives (x−3)² + (y+2)² = 25.
Question 7: A regular hexagon has 6 sides. What is the sum of its interior angles?
- 540°
- 720° (Correct answer)
- 900°
- 1080°
Correct answer: 720°
Sum = (6 − 2) × 180° = 4 × 180° = 720°.
Regents Geometry 4
An inscribed angle in a circle intercepts an arc of 140°.
What is the measure of the inscribed angle?