Bluebook SAT Test Lines, Angles, and Triangles 8 — Questions and Answers
Question 1: An angle is 14° more than its complement. What is the angle?
- 38°
- 52° (Correct answer)
- 62°
- 76°
Correct answer: 52°
x + (x − 14) = 90° → 2x = 104° → x = 52°.
Question 2: Triangle XYZ has angle X = (4k + 5)°, angle Y = (2k + 15)°, angle Z = (6k − 20)°. What is angle Z?
- 50°
- 55°
- 70° (Correct answer)
- 85°
Correct answer: 70°
4k+5+2k+15+6k−20=180 → 12k=180 → k=15; angle Z = 6(15)−20 = 70°.
Question 3: An isosceles triangle has perimeter 50 cm and base 14 cm. What are the two equal sides?
- 14 cm
- 16 cm
- 18 cm (Correct answer)
- 22 cm
Correct answer: 18 cm
2s + 14 = 50 → s = 18 cm.
Question 4: In similar triangles, the ratio of similarity is 3:4. The smaller triangle has altitude 12. What is the larger triangle's altitude?
- 9
- 12
- 16 (Correct answer)
- 18
Correct answer: 16
3/4 = 12/h → h = 48/3 = 16.
Question 5: An exterior angle of a triangle is (5x + 3)°. The two remote interior angles are (2x + 5)° and (x + 6)°. What is x?
- 1
- 3
- 4 (Correct answer)
- 6
Correct answer: 4
5x+3 = (2x+5)+(x+6) → 5x+3 = 3x+11 → 2x=8 → x=4. Check: 5(4)+3=23; (2(4)+5)+(4+6)=13+10=23. ✓
Question 6: Two parallel lines are cut by a transversal. Co-interior angles are (4n + 10)° and (2n + 26)°. What is n?
- 12
- 18
- 24 (Correct answer)
- 30
Correct answer: 24
(4n+10)+(2n+26)=180 → 6n+36=180 → 6n=144 → n=24.
Question 7: Triangle ABC ≅ Triangle DEF (by SAS): AB = DE = 8, angle B = angle E = 50°, BC = EF = 6. What can be concluded?
- The triangles are similar but not necessarily congruent
- AC = DF (Correct answer)
- AB = EF
- Angle A = Angle F
Correct answer: AC = DF
By SAS congruence, all corresponding parts are equal; AC corresponds to DF, so AC = DF.
Bluebook SAT Test Lines, Angles, and Triangles 8
An angle is 14° more than its complement.
What is the angle?