Lines, Angles, and Triangles Flashcards

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.

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°.

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.

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°.

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.

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°.

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.