In a regular polygon with $4$ sides, what is the measure of each interior angle?

• A. $60°$
• B. $45°$
• C. $120°$
• D. $90°$

Answer: (D)

Verified step by step guidance

1. Recall the formula to find the measure of each interior angle of a regular polygon with \( n \) sides: \[ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} \]
2. Identify the number of sides \( n \) in the polygon. Here, \( n = 4 \) since it is a regular polygon with 4 sides.
3. Substitute \( n = 4 \) into the formula: \[ \text{Interior Angle} = \frac{(4 - 2) \times 180^\circ}{4} \]
4. Simplify the numerator first: \[ (4 - 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ \]
5. Divide the result by the number of sides to find each interior angle: \[ \frac{360^\circ}{4} = 90^\circ \]