Four angles of a polygon are 100° each. The remaining angles are 160° each. Find the number of sides of the polygon.

A polygon is a closed two-dimensional figure, that comprises three or more straight lines.

Answer: The number of sides of the polygon is 6.

We know that sum of all interior angles of a polygon = (n – 2) × 180°

Explanation:

Let n be the number of sides of the polygon.

The sum of interior angles of the polygon is = (n – 2) × 180° ---- (1)

The number of angles measuring 100° is 4.

The number of angles measuring 160° is n - 4.

So, sum of interior angles of the given polygon = 4 × 100° + (n - 4) × 160°

= (160° × n) - 240° ---- (2)

Equating (1) and (2), we get

(n – 2) × 180° = (160° × n) - 240°

n (180° - 160°) = 360° - 240°

n = 120 / 20

n = 6

Thus the polygon is a hexagon.

Therefore, the number of sides of the polygon is 6 (Hexagon).