Each exterior angle of a polygon is 30o. Calculate the sum of the interior angles

Analyze the question: We're told each exterior angle of a polygon is 30°, which means the polygon is regular (all exterior angles are equal). We need the sum of its interior angles.

Concept:

• The sum of exterior angles of any polygon is 360°.
• Number of sides: n = 360° ÷ (exterior angle)
• Sum of interior angles = (n − 2) × 180°

Solution:

Step 1: Find the number of sides. n = 360° ÷ 30° = 12 sides

Step 2: Find the sum of the interior angles. Sum = (n − 2) × 180° Sum = (12 − 2) × 180° Sum = 10 × 180° Sum = 1800°

Check: Each interior angle = 180° − 30° = 150°. Then 12 × 150° = 1800°. ✔

Answer: The sum of the interior angles is 1800°, which is option D.

Tip: Always start with n = 360° ÷ exterior angle. Once you have n, plug it into (n − 2) × 180°. Alternatively, remember that the sum of interior angles = n × 180° − 360°, which gives 12 × 180° − 360° = 1800°.