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Lines, Angles, and Triangles Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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

    Answer: 8

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

  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?

    Answer: 50°

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

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

    Answer: 108 cm²

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

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

    Answer: 25.7°

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

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

    Answer: 15

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

  6. Parallel lines p and q are cut by transversal t. An angle at the intersection with p is 112°. What is the supplementary angle at that same intersection?

    Answer: 68°

    Supplementary angles sum to 180°: 180° − 112° = 68°.

  7. Triangle MNP has vertices at M(0, 0), N(6, 0), and P(2, 4). What is the area of the triangle?

    Answer: 12

    Base MN = 6 (along x-axis); height = y-coordinate of P = 4; area = ½(6)(4) = 12.