Question

In the figure, a regular polygon is inscribed in a circle. Using only the segments given in the figure, identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle.

Answer 1

Explanation:

Answer 2

The center, radius, apothem, and central angle of the polygon include:

center: point K.

radius: segment KB.

apothem: segment KM.

central angle: ∠BKA

measure of central angle: 36°.

In Mathematics and Geometry, a polygon is a two-dimensional geometric figure that is typically composed of straight line segments and finite number of sides.

The point located at the middle of the circle represents the center and it should be named point K. The radius is a segment drawn from the center of a circle to its perimeter (side length), so it should either be named segment KB or KA.

The apothem is a segment drawn from the center of the polygon to the midpoint of one of its sides, so it should be named segment KM. Also, a central angle is formed at the center of a circle by the intersection of two radii within the circle such as ∠BKA.

Since this regular polygon (decagon) has 10 sides, the measure of a central angle can be calcuated as follows;

m∠BKA = 360°/10

m∠BKA = 36°.