Parallel Lines Cut by a Transversal

Input

Angle θ — angle ∠1 (degrees, 0°–180°)

This is the acute or obtuse angle at the upper-left intersection.

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Angle Relationships

■ Corresponding: equal (same side, same position)
■ Alternate interior: equal (opposite sides, between lines)
■ Alternate exterior: equal (opposite sides, outside lines)
■ Co-interior: supplementary (same side, between lines)

All 8 Angles

Enter θ to see all 8 angles.

The 8 Angles

When a transversal crosses two parallel lines, it creates 8 angles — 4 at each intersection. They come in pairs related by position and equality.

Angles on the same side of the transversal and same position relative to each line are called corresponding and are always equal.

Angles between the parallel lines on opposite sides are alternate interior angles — always equal.

Key Rules

∠1 = ∠3 = ∠5 = ∠7 (θ) ∠2 = ∠4 = ∠6 = ∠8 (180°−θ)

At each intersection: adjacent angles are supplementary (sum to 180°), and opposite angles are vertical (equal).

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