Find the smaller angle of an isosceles trapezoid, one of the corners of which is 105?

Given:

ABCE – isosceles trapezoid,

angle A = 105 degrees.

Find the degree measures of the angles of the trapezoid ABCE: angle B, angle C, angle E -?

Decision:

Consider an isosceles trapezoid ABCE. Its angles at the base are equal, that is, the angle A = the angle E = 105 degrees and the angle B = the angle C. We know that the sum of the degree measures of the trapezoid is 360 degrees.

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

105 + 105 + 2 * angle B = 360;

210 + 2 * angle B = 360;

2 * angle B = 360 – 210;

2 * angle B = 150 (in order to find an unknown factor, you need to divide the product by a known factor);

angle B = 150: 2;

angle B = 75 degrees.

Answer: 75 degrees.