What is the measure of each interior angle in a regular pentagon?

To find the measure of each interior angle in a regular pentagon, we can use the formula for the interior angle of a regular polygon, which is given by the formula:

[ \text{Interior Angle} = \frac{(n - 2) \times 180°}{n}

]

where ( n ) is the number of sides of the polygon. For a pentagon, ( n = 5 ).

Substituting 5 into the formula, we get:

[ \text{Interior Angle} = \frac{(5 - 2) \times 180°}{5} = \frac{3 \times 180°}{5} = \frac{540°}{5} = 108° ]

This calculation shows that each interior angle in a regular pentagon is 108°. Regular pentagons have equal side lengths and equal angles, which is why each angle is the same.

Understanding this formula and how to apply it helps in calculating interior angles for any regular polygon, not just pentagons. The other choices do not satisfy the formula for a pentagon, confirming that 108° is indeed the correct and only measure for each interior angle in a regular pent