Bluebook SAT Test Lines, Angles, and Triangles 6 — Questions and Answers
Question 1: Line l is parallel to line m. A transversal makes a 48° alternate interior angle with l. What is the corresponding alternate interior angle at m?
- 42°
- 48° (Correct answer)
- 132°
- 138°
Correct answer: 48°
Alternate interior angles formed by parallel lines are equal: 48°.
Question 2: A triangle has sides 7, 24, and 25. Is it a right triangle?
- Yes, because 7 + 24 = 25
- Yes, because 7² + 24² = 25² (Correct answer)
- No, because 7² + 24² ≠ 25²
- Cannot be determined
Correct answer: Yes, because 7² + 24² = 25²
7² + 24² = 49 + 576 = 625 = 25²; it satisfies the Pythagorean theorem.
Question 3: A linear pair of angles measures (3x + 15)° and (x + 25)°. What is x?
- 25
- 30
- 35 (Correct answer)
- 40
Correct answer: 35
(3x+15)+(x+25)=180 → 4x+40=180 → x=35.
Question 4: Two similar triangles have perimeters 30 cm and 45 cm. A side of the smaller is 8 cm. What is the corresponding side of the larger?
- 10 cm
- 12 cm (Correct answer)
- 13.5 cm
- 16 cm
Correct answer: 12 cm
Ratio = 30:45 = 2:3; corresponding side = 8 × 3/2 = 12 cm.
Question 5: Triangle MNP has an exterior angle at M of 130°. Angle N = 70°. What is angle P?
- 50°
- 60° (Correct answer)
- 70°
- 80°
Correct answer: 60°
Exterior at M = angle N + angle P → 130° = 70° + P → P = 60°.
Question 6: BD bisects angle ABC. If angle ABD = 35°, what is angle DBC?
- 35° (Correct answer)
- 55°
- 70°
- 145°
Correct answer: 35°
An angle bisector creates two equal halves; angle DBC = 35°.
Question 7: Adjacent supplementary angles at an intersection are (5x + 10)° and (3x + 30)°. What is x?
- 12
- 14
- 17.5 (Correct answer)
- 20
Correct answer: 17.5
(5x+10)+(3x+30)=180 → 8x+40=180 → 8x=140 → x=17.5.
Bluebook SAT Test Lines, Angles, and Triangles 6
Line l is parallel to line m.
A transversal makes a 48° alternate interior angle with l.
What is the corresponding alternate interior angle at m?