The sum of all interior angles of a 20-sided polygon is:

Correct — A. Diagonals from one vertex split an n-sided polygon into n − 2 triangles, each worth 180°.

Triangles: n − 2 = 20 − 2 = 18
Angle total: 18 × 180° = 3240°

Check with exterior angles: 20 × 180° − 360° = 3600° − 360° = 3240° → option (a)

Why the others are wrong

• (b)
  3600° — 3600° is 20 × 180°, which counts each interior angle together with its exterior angle. Remove the exterior angles, 360° in all, to leave 3240°.
• (c)
  3060° — 3060° is 17 × 180°, the angle total of a 19-sided polygon. It subtracts 3 from n instead of 2.
• (d)
  3420° — 3420° is 19 × 180°, using n − 1 instead of n − 2. That is the angle total of a 21-sided polygon.

Draw every diagonal from one vertex and an n-sided polygon splits into n − 2 triangles. Their angles together make up the polygon's interior angles, so the total is (n − 2) × 180°.

For 20 sides that is 18 triangles and 3240°. The total does not depend on whether the polygon is regular.

Key facts

• Interior angles of an n-sided polygon total (n − 2) × 180°.
• The exterior angles of a convex polygon total 360°.
• A regular 20-sided polygon has interior angles of 162° and exterior angles of 18°.

Common traps

• Multiplying 20 × 180° and forgetting to take away 360°.
• Using n − 1 in place of n − 2, which gives the total for a polygon with one more side.

No directly related past PYQ was found.