Find the angles of an isosceles trapezoid if one of its angles is 30 degrees larger than the other.

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

2. Determine the greater angle of the isosceles trapezoid

(x + 30˚).

3. The sum of the angles of an isosceles trapezoid with a smaller base is equal to:

(x + 30˚) + (x + 30˚) = x + 30˚ + x + 30˚ = 2x + 60˚.

4. The sum of the angles of an isosceles trapezoid with a larger base is equal to:

x + x = 2x.

5. Since the sum of the angles of an isosceles trapezoid is 360˚, then we compose and solve the equation:

2x + 2x + 60˚ = 360˚;

4x + 60˚ = 360˚;

4x = 360˚ – 60˚;

4x = 300˚;

x = 300˚: 4;

x = 75˚.

6. The smaller angle of an isosceles trapezoid is x = 75˚.

7. What is the greater angle of an isosceles trapezoid?

x + 30˚ = 75˚ + 30˚ = 105˚.

Answer: the angles of an isosceles trapezoid are equal to 75˚, 105˚, 75˚, 105˚.