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?
Accepted Solution
A:
Answer:108°Step-by-step 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[tex](n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}[/tex]All interior angles in regular pentagon are of equal measure, so[tex]\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]Thus, the measure of each angle formed by the lights on the perimeter is 108°.