Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Use alternate interior angles with parallel lines
Problem
Given parallel lines cut by a transversal and \(\text{one}~\text{alternate}~\text{interior}~\text{angle}\) is \(74^{\circ}\), use alternate interior angles to find the missing angle measure.
An alternate-interior pair must satisfy two location tests: both angles lie between the parallel lines, and they sit on opposite sides of the transversal. We’ll verify those positions first, invoke congruence from parallelism, and transfer the known measure without supplementary arithmetic.
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