Bluebook SAT Test Lines, Angles, and Triangles 8

Question 1

An angle is 14° more than its complement. What is the angle?

Accepted Answer

52°

Answer

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?

Accepted Answer

70°

Answer

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?

Accepted Answer

18 cm

Answer

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?

Accepted Answer

16

Answer

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?

Accepted Answer

4

Answer

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. ✓

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