If each exterior angle of a regular polygon is 18°, the number of sides is

For any convex polygon, the sum of all exterior angles (one at each vertex, taken in order) is always 360°, no matter how many sides it has. For a REGULAR polygon, every exterior angle is equal, so each exterior angle measures 360° divided by the number of sides n, i.e. exterior angle = 360°/n.

1. Write the identity: sum of exterior angles of any convex polygon = 360°.

2. For a regular polygon with n sides, each exterior angle = 360°/n (the total is shared equally).

3. Substitute the given exterior angle: 360°/n = 18°.

4. Solve for n: n = 360°/18° = 20.

Cross-check using interior angles: interior angle = 180° − 18° = 162°. The sum of interior angles of an n-sided polygon is (n − 2) × 180°. For n = 20: (20 − 2) × 180° = 18 × 180° = 3240°, and 3240°/20 = 162°, which matches the interior angle found above.

So the regular polygon has 20 sides.