The vertices of triangle ABC lie on a circle, angle A = 70 degrees, angle C = 30 degrees.

The vertices of triangle ABC lie on a circle, angle A = 70 degrees, angle C = 30 degrees. What is the degree measure of the smallest of the arcs?

Determine the value of the angle ABC of the triangle ABC.

Angle ABC = (180 – BAC – ACB) = (180 – 70 – 30) = 80.

Then the smallest angle of the triangle is 30.

All angles of a triangle are inscribed angles, so the smallest arc of a circle will be the arc on which the smallest inscribed angle rests.

Arc AB = ACB * 2 = 30 * 2 = 60.

Answer: The smallest arc is 60.