Bluebook SAT Test Lines, Angles, and Triangles 10 — Questions and Answers
Question 1: Point P is inside triangle ABC such that angle PBC = 20° and angle PCB = 30°. If angle BAC = 70°, what is angle BPC?
- 130° (Correct answer)
- 100°
- 110°
- 120°
Correct answer: 130°
In triangle BPC: angle BPC = 180° − 20° − 30° = 130°.
Question 2: A transversal crosses parallel lines forming co-interior angles of (5y − 10)° and (3y + 30)°. What is y?
- 20 (Correct answer)
- 15
- 25
- 10
Correct answer: 20
Co-interior angles sum to 180°: (5y−10)+(3y+30)=180 → 8y+20=180 → y=20.
Question 3: Triangle ABC has angles A = (x + 20)°, B = (2x − 5)°, and C = (x + 45)°. What is angle B?
- 55° (Correct answer)
- 65°
- 45°
- 75°
Correct answer: 55°
Sum = 180°: (x+20)+(2x−5)+(x+45) = 180 → 4x+60 = 180 → x = 30; B = 2(30)−5 = 55°.
Question 4: Two straight lines intersect. One pair of vertical angles is (3k + 7)° and (k + 43)°. What is k?
- 18 (Correct answer)
- 20
- 24
- 15
Correct answer: 18
Vertical angles are equal: 3k+7 = k+43 → 2k = 36 → k = 18.
Question 5: In triangle DEF, DE is the longest side. Which angle must be the largest?
- Angle F (Correct answer)
- Angle D
- Angle E
- All angles are equal
Correct answer: Angle F
The largest angle is opposite the longest side; DE is opposite angle F.
Question 6: Parallel lines a and b are cut by transversal t. The angle at the intersection with a is 148°. What is the size of the alternate exterior angle at b?
- 148° (Correct answer)
- 32°
- 58°
- 180°
Correct answer: 148°
Alternate exterior angles are equal when lines are parallel, so the angle is 148°.
Question 7: A straight angle is divided into three consecutive angles: x, 2x, and 3x. What is the measure of the middle angle?
- 60° (Correct answer)
- 30°
- 90°
- 45°
Correct answer: 60°
x + 2x + 3x = 180° → 6x = 180° → x = 30°; middle angle = 2x = 60°.
Bluebook SAT Test Lines, Angles, and Triangles 10
Point P is inside triangle ABC such that angle PBC = 20° and angle PCB = 30°.
If angle BAC = 70°, what is angle BPC?