Find the number of sides of a regular convex polygon whose exterior angle is…

For any convex polygon, the sum of all exterior angles is always 360°. For a REGULAR polygon with n sides, every exterior angle is equal, so each exterior angle = 360°/n. Also, at each vertex the interior angle and exterior angle form a linear pair: interior angle + exterior angle = 180°.

1. Given: exterior angle = 40°

2. Apply the formula: exterior angle = 360°/n

3. So 40 = 360/n

4. n = 360/40 = 9

Cross-check: for n = 9, exterior angle = 360/9 = 40° (matches). Interior angle = 180 - 40 = 140°. Sum of interior angles = (9-2) × 180 = 1260°, and 9 × 140 = 1260° (matches).

Hence, the regular convex polygon has 9 sides.