In a rectangular trapezoid, the larger of the angles is 40 degrees larger than the smaller.

In a rectangular trapezoid, the larger of the angles is 40 degrees larger than the smaller. Find the degree measure of the greater angle of this trapezoid.

1. According to the problem statement, the trapezoid is rectangular, so the angles at one side are straight.
Larger and smaller angles can be at the second side of the trapezoid.
By the definition of a trapezoid, its bases are parallel. This means that the angles at the lateral side are internal one-sided with parallel bases and secant to the lateral side of the trapezoid.
It is known that the sum of the inner one-sided angles is 180 *
2. Let’s designate the smaller angle as x * and compose an equation if it is known that the larger angle is 40 * greater than the smaller one.
x * + (x * + 40 *) = 180 *;
2 x * = 180 * – 40 * = 140 *;
x = 140 *: 2 = 70 *.
Determine the larger angle
x + 40 * = 70 * + 40 * = 110 *.
Answer: The larger angle of the trapezoid is 110 *.