One corner of an isosceles trapezoid is 9 times larger than the other. Find the obtuse angle of this trapezoid.

Let us introduce the notation:

Let the acute angle of an isosceles trapezoid be x, then the obtuse angle of the trapezoid is 9 * x = 9x.

Let’s compose and solve the equation:

As you know, the sum of the inner one-sided angles is 1800, we get

9x + x = 180,

10x = 180,

x = 1800: 10,

x = 180.

This means that the acute angle of an isosceles trapezoid is 180.

Find the degree measure of the obtuse angle of an isosceles trapezoid:

9 * 180 = 162.

Answer: The obtuse angle of an isosceles trapezoid is 162.