When a straight line (a transversal) crosses two parallel lines it creates eight angles, but only two distinct values appear. Corresponding angles (same position at each intersection) are equal, alternate interior angles (between the parallels, opposite sides of the transversal) are equal, and alternate exterior angles are equal. The one pair that is NOT equal is co-interior (same-side interior) angles: they are supplementary, adding to 180°. A reliable shortcut is that every one of the eight angles is either equal to your reference angle or supplementary to it — so each angle is one of just two numbers that themselves add to 180°. The GRE often marks the lines parallel with matching arrowheads; use those marks, not the drawing, since it is not to scale.
✅ Solved examples
1. Two parallel lines are cut by a transversal. One angle measures 65°. Find its corresponding angle.
Corresponding angles are equal, so the corresponding angle is also 65°.
2. Two parallel lines are cut by a transversal. A co-interior (same-side interior) angle is 110°. Find the other co-interior angle.
Co-interior angles are supplementary: 180° − 110° = 70°.
3. Alternate interior angles are (3x − 5)° and (2x + 20)°. Find x and the angle measure.
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