If the measure of an exterior angle of a regular polygon is 20°, determine the total number of its sides.

Correct — B.
The exterior angles of a convex polygon add up to 360°
A regular polygon has n equal exterior angles: n × 20° = 360°
Divide: n = 360 ⁄ 20 = 18

Check with the interior angle: 180° − 20° = 160°
(18 − 2) × 180° ⁄ 18 = 2880° ⁄ 18 = 160° → option (b)

Why the others are wrong

• (a)
  15 — A regular 15-gon has exterior angles of 360° ⁄ 15 = 24°, not 20°.
• (c)
  20 — 20 repeats the angle given in the question. A regular 20-gon has exterior angles of 360° ⁄ 20 = 18°, not 20°.
• (d)
  36 — A regular 36-gon has exterior angles of 360° ⁄ 36 = 10°, half of the 20° given.

Walk once around a convex polygon and you turn through one full circle, so its exterior angles sum to 360° whatever the number of sides.

In a regular polygon those angles are equal, so exterior angle = 360° ⁄ n, and n = 360° ⁄ exterior angle. The interior angle is the supplement, 180° − exterior, which gives a second route and a check.

Key facts

• Sum of the exterior angles of a convex polygon = 360°
• Regular polygon: n = 360° ⁄ (one exterior angle)
• Interior angle + exterior angle = 180° at each vertex
• Sum of the interior angles of an n-sided polygon = (n − 2) × 180°

Common traps

• Dividing 360° by the interior angle instead of the exterior one.
• Marking 20, the number given in the question. Because 20 × 18 = 360, a regular 20-gon has 18° exterior angles: the two numbers swap roles.

No directly related past PYQ was found.