The vertices of the triangle ABC lie on a circle, angle A = 50, angle B = 45. What is the degree measure of the arc AB?

We find out the value of the angle ACB of the triangle ABC.

The sum of the inner angles of the triangle is 180, then the angle ACB = 180 – CAB – ABC = 180 – 50 – 45 = 85.

The inscribed angle ACB rests on the arc AB, then the degree measure of the arc AB will be equal to two values of the inscribed angle resting on this arc.

Arc AB = 2 * 85 = 170.

Answer: The degree measure of the arc AB is 170.