Question

The sum of exterior angles in a polygon is twice the sum of the interior angles.

(i) Find how many sides the polygon has?

(ii) Find the number of sides, if the sum of the exterior angles is half of the sum of the interior angles.

(iii) Find the number of sides if the sum of the exterior angles is equal to the sum of the interior angles?

Answer 1

The sum of exterior angles in a polygon is 360°.

(i) The sum of the interior angles in a triangle is 180°. It is a triangle and has 3 sides.

(ii) If the sum of the interior angles is 720°, the polygon has six sides.

(iii) If the sum of the interior angles is 360°, the polygon is a quadrilateral it has 4 sides.