Angles of a Trapezoid

Angles of a Trapezoid

How to solve the interior angles of a trapezoid problems: property, example, and its solution.

Definition

A trapezoid is a quadrilateral that have a pair of parallel sides.

A trapezoid is a quadrilateral
that have a pair of parallel sides.

Base: parallel sides
Legs: non-parallel sides

Property

The sum of the measures of the consecutive interior angles is 180.

The sum of the measures
of the consecutive interior angles is 180.
(purple & blue angles)

This is true because those two angles are
the consecutive interior angles in parallel lines.

To use this formula,
the angles have to include the leg.
(not the base)

Example

Find the values of x and y. The measures of the interior angles: 60, x + 40, 8y, 108.

m∠(purple) + m∠(blue) = 180

(x + 40) + 60 = 180

m∠(purple dot) + m∠(blue dot) = 180

8y + 108 = 180