Question

For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

• A. 396
• B. 324
• C. 216
• D. 144

Hint:

Memorize: A regular polygon with more sides always has larger interior angles; formula = $\frac{(n-2)180}{n}$.

Answer 1

The Correct Option is D

For a regular polygon with $n$ sides, the measure of each interior angle is given by the formula: \[ \text{Interior angle} = \frac{(n-2)\times 180^\circ}{n} \] Substituting $n = 10$ for a regular decagon: \[ \text{Interior angle} = \frac{(10 - 2) \times 180^\circ}{10} = \frac{8 \times 180^\circ}{10} \] \[ = \frac{1440^\circ}{10} = 144^\circ \] Thus, each interior angle of a regular 10-sided polygon is 144 degrees.