Bluebook SAT Test Lines, Angles, and Triangles 9 — Questions and Answers
Question 1: In triangle ABC, side AB = 7, BC = 24, and angle B = 90°. What is the length of AC?
- 25 (Correct answer)
- 17
- √575
- 31
Correct answer: 25
AC = √(AB² + BC²) = √(49 + 576) = √625 = 25.
Question 2: Two angles of a triangle are 54° and 78°. A line is drawn from the third vertex perpendicular to the opposite side. What is the measure of the third angle of the triangle?
- 48° (Correct answer)
- 42°
- 52°
- 36°
Correct answer: 48°
Third angle = 180° − 54° − 78° = 48°.
Question 3: Parallel lines r and s are cut by a transversal. A co-interior angle on line r measures (6x + 5)° and the co-interior angle on line s measures (4x + 15)°. What is x?
- 16 (Correct answer)
- 18
- 14
- 20
Correct answer: 16
Co-interior angles are supplementary: (6x+5)+(4x+15) = 180 → 10x+20 = 180 → x = 16.
Question 4: An angle bisector divides a 136° angle into two equal parts. What is the measure of each part?
- 68° (Correct answer)
- 44°
- 56°
- 90°
Correct answer: 68°
Each part = 136° / 2 = 68°.
Question 5: Triangle XYZ is similar to triangle PQR. If XY = 12, YZ = 16, and PQ = 9, what is QR?
- 12 (Correct answer)
- 16
- 8
- 10
Correct answer: 12
Ratio = PQ/XY = 9/12 = 3/4; QR = YZ × 3/4 = 16 × 3/4 = 12.
Question 6: Lines m and n are parallel. A transversal creates an angle of 117° on line m. What is the measure of the alternate interior angle on line n?
- 117° (Correct answer)
- 63°
- 73°
- 107°
Correct answer: 117°
Alternate interior angles are equal when lines are parallel, so the angle is 117°.
Question 7: In a right triangle, the two acute angles are in the ratio 1:5. What is the measure of the larger acute angle?
- 75° (Correct answer)
- 60°
- 80°
- 65°
Correct answer: 75°
Two acute angles sum to 90°; ratio 1:5 → 6 parts = 90° → each part = 15°; larger = 5 × 15° = 75°.
Bluebook SAT Test Lines, Angles, and Triangles 9
In triangle ABC, side AB = 7, BC = 24, and angle B = 90°.
What is the length of AC?