Calculadora de ângulos de trapézio

A trapezoid (US English, called "trapezium" in UK English) has two parallel sides (the bases) and two non-parallel sides (the legs). Because of the parallel-side property, the four interior angles follow a predictable pattern: the two angles on each leg are supplementary, meaning they sum to 180°. Combined with the universal "interior angles of any quadrilateral sum to 360°" rule, knowing just one angle of a trapezoid often determines several others.

The angle rule — co-interior pairs

Label the trapezoid ABCD so that AB and CD are the two parallel bases. Then AD and BC are the legs.

Imagine AB and CD as parallel lines. Each leg (AD and BC) is a transversal cutting through both. By the co-interior angle theorem for parallel lines + transversal, the two angles on each side of a transversal between the parallel lines sum to 180°:

• ∠A + ∠D = 180° (the two angles at the left leg AD)
• ∠B + ∠C = 180° (the two angles at the right leg BC)

Adding both pairs: ∠A + ∠B + ∠C + ∠D = 360°, the universal quadrilateral angle sum — verifying consistency.

Worked example — finding all angles

Trapezoid with ∠A = 70°. Find the other three angles, assuming ABCD is a general trapezoid (only AB ∥ CD given, no other special properties).

From ∠A + ∠D = 180°: ∠D = 110°.

The other two angles (B and C) are not yet determined — we only have one constraint (∠B + ∠C = 180°) and infinitely many pairs satisfy it. We need an additional given value or assumption (like "isosceles trapezoid", which forces ∠B = ∠A = 70° by symmetry).

If we ALSO assume ∠B = 100°, then ∠C = 80°.

Why opposite angles are NOT generally equal

In a parallelogram, opposite angles ARE equal — because both pairs of opposite sides are parallel, so BOTH legs serve as transversals between parallel lines.

In a trapezoid, only ONE pair of sides is parallel. Only ONE set of co-interior angle equalities holds (the one on the parallel-side transversal). The opposite-angle equality of parallelograms does not carry over.

Special trapezoid types

Right trapezoid

A right trapezoid has two adjacent right angles — say ∠A = ∠D = 90°. The other two angles (∠B and ∠C) sum to 180° by the co-interior rule on leg BC.

Example: ∠A = 90°, ∠D = 90°, ∠B = 120° → ∠C = 60°.

Isosceles trapezoid

An isosceles trapezoid has the two legs equal in length, which forces the two base angles on each base to be equal:

∠A = ∠B (both on base AB) and ∠C = ∠D (both on base CD).

Combined with the co-interior rule, knowing one angle determines all four. If ∠A = 70°, then ∠B = 70°, ∠C = ∠D = 110°.

See the Isosceles Trapezoid Calculator for more on this type.

Scalene trapezoid

No equal legs or right angles — just the basic "one pair parallel sides" definition. The co-interior rule still applies; the only constraint on angles is the supplementary pairs along each leg.

Verifying you really have a trapezoid

If a quadrilateral satisfies the co-interior angle rule (∠A + ∠D = 180° and ∠B + ∠C = 180°), it must have one pair of parallel sides — so it IS a trapezoid. Conversely:

• If only ONE pair of co-interior pairs sums to 180° (say ∠A + ∠D = 180°), then AB ∥ CD. The other pair of sides (BC, AD) may or may not be parallel.
• If BOTH pairs sum to 180° (which would mean ∠A + ∠D + ∠B + ∠C = 360° AND ∠A + ∠B + ∠C + ∠D = 360° — just the same equation), you have a parallelogram or trapezoid depending on side lengths.

Exterior angles

Each interior angle has a corresponding exterior angle (supplementary). For trapezoids:

• Sum of all 4 exterior angles = 360° (true for any convex polygon)
• Each exterior pair on a leg sum to 180° (supplements of interior angles already summing to 180°)

Co-interior vs alternate-interior — quick recap

For trapezoid angle problems specifically, you need the co-interior pair (sum to 180°). The other relations apply to angles formed elsewhere in the figure (e.g., when a diagonal is drawn).

Worked example — right trapezoid in construction

A right trapezoid serves as the side profile of a wedge ramp. The base is 10 m long, the top is 4 m, and one side is a vertical wall (perpendicular). The angles are ∠A = ∠D = 90° (wall corners) and ∠B + ∠C = 180° (the slope-end leg).

If the slope-end leg makes a 70° angle with the longer base (∠C = 70°), then ∠B = 110°. The angle of inclination of the slope is 70°.

Common mistakes

• Assuming opposite angles are equal. True only for parallelograms (both pairs of opposite sides parallel). Trapezoids have only co-interior pairs along legs, not opposite-angle equality.
• Using interior + interior = 180° for the wrong pair. The supplementary pair is the two angles on the SAME leg, not the two angles on the same base. Always check which pair the problem is asking about.
• Forgetting the total 360°. The four interior angles must sum to 360°. After finding any 3, the 4th is determined.
• Treating a parallelogram's angle rule as a trapezoid rule. A parallelogram has 2 pairs of parallel sides (so 4 co-interior pairs around the figure). A trapezoid has only 1 pair (so only 2 co-interior pairs). The trapezoid is less constrained.