CAT Polygon - Practice Questions & MCQ

Polygons are all around us. A stop sign is in the shape of an octagon, an eight-sided polygon. The honeycomb of a beehive consists of hexagonal cells. The top of a desk is a rectangle.

A closed plane figure bounded by line segments is called a polygon. Poly means 'many', so a polygon is a closed many sided figure.

Polygons are classified as follows with reference to the number of sides they have:

Convex polygon: In a convex polygon each interior angle is less than 180°.

Concave polygon: In this type of a polygon at least one of the interior angles is a reflex angle, i.e., greater than 180°.

Regular polygon: A polygon is regular if: (i) it is convex (ii) all of its sides are equal (iii) all of its interior angles are equal.

In case, all the sides are not equal, then the polygon is called an irregular polygon.

Exterior Angle of a Polygon

An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side.

Some Important Results on Polygons

1. Diagonals of a polygon: A line segment joining any two non-consecutive vertices of a polygon is called it's diagonal. The number of diagonals of a polygon with n sides is given by .

2. The sum of all the exterior angles of a polygon is 360°.
3. The number of diagonals of a polygon with n sides is given by (2n – 4) 90°.
4. Each interior angle of a regular polygon of n sides is .
5. Each exterior angle of a regular polygon of n sides is .
6. The number of sides n of a regular polygon whose exterior angle x° is .