Find the angular measure of the arc AB, BC, AC if the degree measures of the corresponding or central

Find the angular measure of the arc AB, BC, AC if the degree measures of the corresponding or central angles are equal: angle AOB = 30 degrees, angle BOC = 70 degrees.

The problem has two solutions depending on the location of points A, B, C on the circle.

Since we are given the values of the central angles. Then the degree measures of the arcs on which the central angles are based are equal to the degree measures of these angles.

Then in Fig. 1 arc AB = 30, arc BC = 700, smaller arc AC = 70 + 30 = 1000, large arc AC = 360 – 70 – 30 = 260.

In fig. 2 arc AB = 30, arc BC = 70, smaller arc AC = 70 – 30 = 40, large arc AC = 360 – 40 = 320.