What is the measure of each intercepted arc for each inscribed angle of a regular hexagon inscribed in a circle?

Question

What is the measure of each intercepted arc for each inscribed angle of a regular hexagon inscribed in a circle?

Answer 1

Hi San!

You want the measure of the intercepted arcs so, what does the inscribed angle theorem say about inscribed arcs? The measure of the inscribed angle is half the measure of its intercepted arc. Or measure of arc is 2 x measure of angle.

So now we need to find the measure of the inscribed angle. We can use the Sum of the Measure of Interior Angles = (n-2) x 180; with n = number of sides.

Sum = (6-2) x 180 = 720 / 6 angles = 120 degrees each angle

Measure of intercepted arc is 2x measure of angle

Intercepted arc = 120 x 2 = 240 degrees

I hope this makes sense, let me know if you have any questions.