Angles of an Isosceles Trapezoid

Angles of an Isosceles Trapezoid

How to solve the angles of an isosceles trapezoid problems: properties, example, and its solution.

Definition

An isosceles trapezoid is a trapezoid whose legs are congruent. Its base angles are also congruent.

An isosceles trapezoid is a trapezoid
whose legs are congruent.

Its base angles (blue angles) are also congruent,
just like an isosceles triangle.

Properties

The base angles are congruent (same colored angles). The sum of the measures of the consecutive interior angles is 180.

There are two properties
related to the angles of an isosceles trapezoid.

The base angles are congruent.
(= Same colored angles are congruent.)

An isosceles trapezoid is also a trapezoid.
So the sum of the measures
of the consecutive interior angles is 180.
(purple & blue angles)

Angles of a trapezoid

Example

Find the measure of angle A, B, and C. The measure of angle D: 60.

D and ∠C are the base angles,
which are congruent.

So m∠D = m∠C = 60.

A and ∠D are the consecutive interior angles.

So m∠A + m∠D = 180.
m∠A + 60 = 180.

A and ∠B are the base angles,
which are congruent.

So m∠A = m∠B = 120.