Bluebook SAT Test Lines, Angles, and Triangles 5 — Questions and Answers
Question 1: A ray divides a straight angle into two angles, one of which is 5 times the other. What is the larger angle?
- 30°
- 60°
- 120°
- 150° (Correct answer)
Correct answer: 150°
x + 5x = 180° → x = 30°; larger = 5 × 30° = 150°.
Question 2: Parallel lines are cut by a transversal. One co-interior angle is 73°. What is the other?
- 73°
- 107° (Correct answer)
- 117°
- 127°
Correct answer: 107°
Co-interior angles are supplementary: 180° − 73° = 107°.
Question 3: Triangle GHI ~ Triangle JKL. GH = 10, HI = 14, JK = 5. What is KL?
- 3.5
- 7 (Correct answer)
- 9
- 28
Correct answer: 7
Scale factor = GH/JK = 10/5 = 2; KL = 14/2 = 7.
Question 4: The interior angles of triangle are (x + 10)°, (2x − 10)°, and (3x − 60)°. What is x?
- 30
- 35
- 40 (Correct answer)
- 50
Correct answer: 40
(x+10)+(2x−10)+(3x−60)=180 → 6x−60=180 → x=40. Check: 50°+70°+60°=180°. ✓
Question 5: Two parallel lines are cut by a transversal. Alternate interior angles are (6x + 3)° and (8x − 15)°. What is x?
- 6
- 9 (Correct answer)
- 12
- 15
Correct answer: 9
6x + 3 = 8x − 15 → 18 = 2x → x = 9.
Question 6: A triangle's angles are in ratio 1:2:3. What type of triangle is it?
- Acute
- Equilateral
- Obtuse
- Right (Correct answer)
Correct answer: Right
k+2k+3k=180° → k=30°; angles are 30°, 60°, 90° — a right triangle.
Question 7: An exterior angle of a triangle is (9x − 3)°. The two remote interior angles are (4x + 7)° and (3x + 14)°. What is x?
- 4
- 6
- 8
- 12 (Correct answer)
Correct answer: 12
9x − 3 = (4x+7)+(3x+14) → 9x−3 = 7x+21 → 2x=24 → x=12. Check: 9(12)−3=105; 4(12)+7+3(12)+14=55+50=105. ✓
Bluebook SAT Test Lines, Angles, and Triangles 5
A ray divides a straight angle into two angles, one of which is 5 times the other.
What is the larger angle?