A regular polygon with $6$ sides is inscribed in a circle. What is the measure of each interior angle of the polygon?

• A. $150°$
• B. $108°$
• C. $135°$
• D. $120°$

Answer: (D)

Verified step by step guidance

1. Recall that a regular polygon has all sides and all interior angles equal.
2. Use the formula for the measure of each interior angle of a regular polygon with n sides: \(\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}\).
3. Substitute \(n = 6\) (since the polygon has 6 sides) into the formula: \(\text{Interior Angle} = \frac{(6-2) \times 180^\circ}{6}\).
4. Simplify the expression step-by-step: calculate \((6-2) = 4\), then multiply \(4 \times 180^\circ = 720^\circ\), and finally divide \(720^\circ\) by \$6$.
5. The result gives the measure of each interior angle of the regular hexagon.