Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Use same-side interior angles with parallel lines
Problem
Given \(\text{one}~\text{same}\text{-}\text{side}~\text{interior}~\text{angle}\) is \(112^{\circ}\), use same-side interior angles to find the missing angle measure.
Same-side interior angles lie between the parallel lines on one side of the transversal, so they are supplementary rather than congruent. We’ll verify that placement, write their sum as a straight-angle total, isolate the missing measure by subtraction, and add back to check.
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