Question

A cricular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed by the lights on the perimeter?

Answer 1

D. 108

Explanation:

I just did the test yourself

Answer 2

108°

Explanation:

Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).

The sum of all interior angles of pentagon can be calculated using following formula

`(n-2)\cdot 180^(\circ),\\ \\(5-2)\cdot 180^(\circ)=3\cdot 180^(\circ)=540^(\circ)`

All interior angles in regular pentagon are of equal measure, so

`(540^(\circ))/(5)=108^(\circ)`

Thus, the measure of each angle formed by the lights on the perimeter is 108°.