In a regular pentagon, what is the sum of any two of its interior angles?

• A. $180°$
• B. $252°$
• C. $216°$
• D. $144°$

Answer: (C)

Verified step by step guidance

1. Recall that a regular pentagon has 5 equal interior angles, and the sum of the interior angles of any polygon with n sides is given by the formula: \(\text{Sum of interior angles} = (n - 2) \times 180^\circ\).
2. Substitute \(n = 5\) into the formula to find the total sum of the interior angles of the pentagon: \(\text{Sum} = (5 - 2) \times 180^\circ\).
3. Calculate the sum of the interior angles: \$3 \times 180^\circ$.
4. Since the pentagon is regular, each interior angle is equal, so divide the total sum by 5 to find the measure of one interior angle: \(\text{Each angle} = \frac{3 \times 180^\circ}{5}\).
5. To find the sum of any two interior angles, multiply the measure of one interior angle by 2: \$2 \times \text{Each angle}$.