Each of the interior angles of a regular polygon is 140°. Calculate the sum of all the interior angles of the polygon.

Analyze the question: We're told each interior angle of a regular polygon is 140°. We need the sum of all interior angles, so we first need the number of sides.

Concept:

• Exterior angle = 180° − interior angle
• Number of sides: n = 360° ÷ exterior angle
• Sum of interior angles = (n − 2) × 180°

Solution:

1. Exterior angle = 180° − 140° = 40°
2. Number of sides: n = 360° ÷ 40° = 9
3. Sum of interior angles = (9 − 2) × 180° = 7 × 180° = 1260°

Check: Each angle is 140°, and there are 9 angles, so 9 × 140° = 1260°. ✓

1260°**.

Tip: For regular polygon questions, find the exterior angle first (180° − interior), then divide 360° by it to get n. Once you have n, you can quickly check your answer by multiplying n by the interior angle.