Question

Lines p and q are parallel.

Parallel lines p and q are cut by transversals r and s. At the intersection of lines p, r, and s, clockwise from top left, the angles are blank, 93 degrees, blank, blank, 1, 60 degrees. At the intersection of lines q and s, the angles are blank, 2, blank, blank. At the intersection of r and q, the angles are 3, blank, blank, blank.

What is the measure of angle 3 in degrees?
27°
33°
60°
153°

Answer 1

27°

Explanation: At the top intersection (where p, r, s meet) the six angles around the point occur in three equal vertical pairs. Clockwise they are: ?, 93°, 60°, ?, (angle 1), 60°. Vertical-opposite equality gives angle 1 = 93° and the angle opposite the 60° is also 60°. Let x be the remaining angle (top-left); its vertical opposite is the other x. Summing around the point: x + 93 + 60 + x + 93 + 60 = 360, so 2x + 306 = 360, hence x = 27°.

Angle 3 at the intersection of r and q is a corresponding angle to that top-left angle (p ∥ q), so angle 3 = 27°.