# The sum of the two angles of an isosceles trapezoid is 236 degrees. Find the smaller angle of the trapezoid

Let an isosceles trapezoid ABCD with bases AD and BC be given. 1. Since the bases of the trapezoid are parallel, then ∠A + ∠B = 180 °, since they are one-sided angles formed at the intersection of two parallel lines AD and BC secant AB. And since ∠B = ∠C, then ∠A + ∠C = 180 °. Thus: ∠A + ∠D = 236 °. Since ∠A = ∠D, we denote them as x: x + x = 236 °; 2 * x = 236 °; x = 236 ° / 2; x = 118 °. Then: ∠A = ∠D = x = 118 °. 1. Find the degree measure ∠B: ∠A + ∠B = 180 °; 118 ° + ∠B = 180 °; ∠B = 180 ° – 118 °; ∠B = 62 °. 1. ∠A… ∠B; 118 °> 62 °, so ∠B = ∠C is a smaller angle. Answer: ∠B = ∠C = 62 °. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.