A regular hexagon is inscribed in a circle as shown. Determine the measure of ∠APB.
To determine the measure of ∠APB, we must first determine the measure of the central angle of the hexagon, which is 60 degrees since the sum of the interior angles of a hexagon is 180 degrees, and there are 6 interior angles in a hexagon.
Next, we know that the angle formed between a chord and a tangent at the point of contact is equal to half the central angle that the chord subtends, which means ∠APB is half the measure of the central angle.
Therefore, ∠APB = 60 degrees / 2 = 30 degrees.
So, the measure of ∠APB is 30 degrees.