Bluebook SAT Test Lines, Angles, and Triangles 16

Question 1

Two parallel lines are cut by a transversal. The alternate interior angles are (5x + 12)° and (3x + 28)°. What is x?

Accepted Answer

8

Answer

Alternate interior angles are equal: 5x+12 = 3x+28 → 2x = 16 → x = 8.

Question 2

In triangle ABC, angle A = 40° and angle B = 65°. A perpendicular is dropped from C to AB at point D. What is angle ACD?

Accepted Answer

50°

Answer

Angle C = 180−40−65 = 75°; in right triangle ACD: angle ACD = 90° − 40° = 50°.

Question 3

Triangles ABC and DEF are similar. AB = 18, DE = 12. The area of DEF is 48 cm². What is the area of ABC?

Accepted Answer

108 cm²

Answer

Ratio = 18/12 = 3/2; area ratio = (3/2)² = 9/4; area ABC = 48 × (9/4) = 108 cm².

Question 4

A set of angles at a point are 5a, 3a, 4a, and 2a. What is a?

Accepted Answer

25.7°

Answer

Angles at a point sum to 360°: 5a+3a+4a+2a = 14a = 360° → a = 360/14 ≈ 25.7°.

Question 5

In right triangle XYZ with right angle at Y, XZ = 17 and YZ = 8. What is XY?

Accepted Answer

15

Answer

XY = √(XZ² − YZ²) = √(289 − 64) = √225 = 15.

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