Question

the interior angle of a regular pentagon can be calculated by:
a ( 5\times180^{circ} )
b ( 180^{circ}div5 )
c ( (5 - 2)\times180^{circ}div5 )
d ( 5\times(180^{circ}div5) )

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The sum of interior angles of a polygon with \(n\) sides is \((n - 2)\times180^{\circ}\). For a pentagon, \(n = 5\), so the sum is \((5 - 2)\times180^{\circ}\).

Step2: Find the measure of one interior angle of a regular pentagon

Since a regular pentagon has all interior angles equal, we divide the sum of interior angles by the number of sides \(n\). So one interior angle is \((5 - 2)\times180^{\circ}\div5\).

Answer:

C. \((5 - 2)\times180^{\circ}\div5\)