Find the angles of an isosceles trapezoid if one of its angles is 30 ° greater than the other.

1. Let’s denote the degree measure of the smaller angle of an isosceles trapezoid through x.

2. Define the degree measure of the greater angle of the isosceles trapezoid:

(x + 30˚).

3. Since the sum of the inner one-sided angles is 180˚, we compose and solve the equation:

(x + 30˚) + x = 180˚;

x + 30˚ + x = 180˚;

2x + 30˚ = 180˚

2x = 180˚ – 30˚;

2x = 150˚;

x = 150˚: 2;

x = 75˚.

4. The degree measure of the smaller angle of an isosceles trapezoid is x = 75˚.

5. What is the degree measure of the greater angle of an isosceles trapezoid?

180˚ – 75˚ = 105˚.

Answer: the degree measures of the angles of an isosceles trapezoid are 75˚, 105˚, 75˚, 105˚.