How do you find the angle measures of a trapezoid?

A trapezoid is a 4-sided shape, therefore the sum of the angles adds to 360 degrees.

if you continue the lines until they touch you have a triangle, whose angles sum to 180 degrees.

using the law of sines, the ratio of length of a side to the sine of the angle opposite of a triangle is consistent for all three sides.

using the law of cosines you are able to find the angle between any two lengths of a triangle.

use these two laws to find the bottom two angles which form the base of the triangle.

the remaining two angles can be found by finding the angles in the triangle that sits on top of the trapezoid, and determining their compliment angle

180 - angle = compliment angle