Bluebook SAT Test Lines, Angles, and Triangles 2 — Questions and Answers
Question 1: In triangle ABC, angle A = 2x, angle B = x + 15, angle C = x + 45. What is x?
- 20
- 24
- 30 (Correct answer)
- 36
Correct answer: 30
2x + (x+15) + (x+45) = 180 → 4x + 60 = 180 → x = 30.
Question 2: Two similar triangles have sides in the ratio 2:5. The shorter triangle has a base of 8 cm. What is the base of the larger triangle?
- 10 cm
- 16 cm
- 20 cm (Correct answer)
- 40 cm
Correct answer: 20 cm
2/5 = 8/b → b = 40/2 = 20 cm.
Question 3: Lines m and n are parallel. A transversal makes a 55° angle with m. What is the alternate exterior angle at n?
- 35°
- 55° (Correct answer)
- 125°
- 135°
Correct answer: 55°
Alternate exterior angles formed by parallel lines are equal: 55°.
Question 4: What is each interior angle of an equilateral triangle?
- 45°
- 60° (Correct answer)
- 90°
- 120°
Correct answer: 60°
Three equal angles sum to 180°; 180° ÷ 3 = 60°.
Question 5: Two complementary angles are in the ratio 1:4. What is the larger angle?
- 18°
- 36°
- 54°
- 72° (Correct answer)
Correct answer: 72°
x + 4x = 90° → x = 18°; larger angle = 72°.
Question 6: In a right triangle, one acute angle is 35°. What is the other acute angle?
- 35°
- 45°
- 55° (Correct answer)
- 65°
Correct answer: 55°
Two acute angles sum to 90°; 90° − 35° = 55°.
Question 7: Triangle PQR ≅ Triangle XYZ. Angle P = 70°, angle Q = 60°. What is angle Z?
- 50° (Correct answer)
- 60°
- 70°
- 180°
Correct answer: 50°
Angle R = 180° − 70° − 60° = 50°; Z corresponds to R, so angle Z = 50°.
Bluebook SAT Test Lines, Angles, and Triangles 2
In triangle ABC, angle A = 2x, angle B = x + 15, angle C = x + 45.
What is x?