Question

Parallel lines r and s are cut by two transversals, parallel lines t and u.

Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of r and u, 13, 14, 15, 16.

How many angles are alternate interior angles with angle 9?

Answer 1

1 — only angle 15.

Reason: alternate interior angles must lie between r and s and be on opposite sides of the same transversal. Angle 9 (at s ∩ u) and angle 15 (at r ∩ u) satisfy this for transversal u; no other angle does.