What is the total measure of all interior angles in a ten-sided polygon?

Correct — B. Split the polygon into triangles from one vertex.

Triangles formed: n − 2 = 10 − 2 = 8
Angles in each triangle: 180°
Multiply: 8 × 180° = 1440° → option (b)

Check with exterior angles, which total 360°: 10 × 180° − 360° = 1440°.

Why the others are wrong

• (a)
  540° — 540° is (5 − 2) × 180°, the angle total of a pentagon. A ten-sided polygon splits into 8 triangles, not 3.
• (c)
  720° — 720° is (6 − 2) × 180°, a hexagon's total. It is also what 90° in place of 180° gives: 8 × 90° = 720°.
• (d)
  900° — 900° is (7 − 2) × 180°, the total for a seven-sided polygon. Ten sides give 8 triangles, so 8 × 180° = 1440°.

Sum of interior angles = (n − 2) × 180°, where n is the number of sides.

The reason: diagonals drawn from one vertex cut an n-sided polygon into n − 2 triangles, and each triangle contributes 180°. Ten sides give 8 triangles, so 1440°.

Key facts

• Sum of interior angles of an n-sided polygon = (n − 2) × 180°.
• The exterior angles of a convex polygon total 360°.
• Each interior angle of a regular decagon is 1440° ÷ 10 = 144°.

Common traps

• Using n × 180° (1800° here) instead of (n − 2) × 180°.
• Using 90° per triangle instead of 180°, which halves the total to 720°.
• Dividing by n when the question asks for the total, not each angle.

No directly related past PYQ was found.