Question

A regular 13-gon is inscribed in a circle. Find the measure of each are intercepted by the sides of the polygon. Round your answer to the nearest hundreth of a degree.

Answer 1

The measure of the angle subtended by each arc intercepted by the sides of the reh13-gon is approximately 27.69°

Explanation:

The number of of equal sides in a regular 13-gon = 13 sides

The measure of the angle, 'θ', subtended by each arc intercepted by the sides of the 13-gon is given as follows;

θ = 360°/13 =
`27(9)/(13) ^(\circ)`

By rounding rounding the answer to the nearest 10th, we have that the measure of the angle subtended by each arc intercepted by the sides of the 13-gon, θ =
`27(9)/(13) ^(\circ)` ≈ 27.69°