Question

The sum of the interior angles of polygons of sides 3, 4, 5 and so on. And the sum of their exterior angles.

Answer 1

Sum of the interior angles of a polygon with n sides = (n − 2) × 180°

Sum of the interior angles of a polygon with 3 sides = (3 − 2) × 180° = 1 × 180° = 180°

Sum of the interior angles of a polygon with 4 sides = (4 − 2) × 180° = 2 × 180° = 360°

Sum of the interior angles of a polygon with 5 sides = (5 − 2) × 180° = 3 × 180° = 540°

Sum of the interior angles of a polygon with 6 sides = (6 − 2) × 180° = 4 × 180° = 720°

…

So, we get the number sequence as:

180, 360, 540, 720, …

The sum of the exterior angles of a polygon with any number of sides is 360°.

So, we get the number sequence as:

360, 360, 360, 360, …