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

An isosceles (or isosceles) trapezoid is a trapezoid whose sides are equal.

In an isosceles trapezoid, the angles at the base are equal.

Let x ° be each angle at the lower base. Then (x + 30) ° is equal to each angle at the upper base of the trapezoid.

The angles in a trapezoid add up to 360 °. Let’s write the equality:

2x + 2 * (x + 30) = 360.

Let’s solve the equation:

2x + 2x + 60 = 360;

4x = 360 – 60;

4x = 300;

x = 300: 4;

x = 75.

The angles at the lower base of the trapezoid are equal at x = 75 °.

Then 75 + 30 = 105 ° are the angles at the upper base.

Answer: 75 ° and 105 °.