Find the obtuse angle of a rectangular trapezoid if the acute angle is 38 °.

Given:

rectangular trapezoid ABCE,

angle E = 38 degrees,

Find the degree measure of the obtuse angle of the trapezoid ABCE, that is, the angle C -?

Decision:

Consider a rectangular trapezoid ABCE. We know that the sum of the degree measures of a trapezoid is 360 degrees. Since it is given that the trapezoid ABCE is rectangular, then the angle A and the angle B are 90 degrees.

Hence:

angle A + angle B + angle C + angle E = 360;

90 + 90 + + angle С + 38 = 360;

180 + angle С + 38 = 360;

208 + angle C = 360;

angle С = 360 – 208;

angle C = 152 degrees.

Answer: 152 degrees.