How Many Angles Does A Quadrilateral Have

Introduction

Before you count the number of angles that a quadrilateral has, let us understand what a quadrilateral is and what its properties are. Well, do you know how many angles are formed when any two lines intersect? As such you must be aware of the concepts of different types of angles such as the interior angles, exterior angles, vertically opposite angles, etc. There are various forms of geometric figures, among which one is your quadrilateral. Every geometric shape is different from each other in terms of the number of its sides, the count of its angles, etc. Let's examine it further by diving in.

The Quadrilateral: Why is it Important?

The importance of the geometric figure named quadrilateral can be understood from the following points.

• Any figure having four sides is categorized as a quadrilateral which is very common in our day-to-day life.

• There are different types of quadrilaterals that you may come across in geometry.

• Every quadrilateral has two diagonals.

• Each diagonal of the quadrilateral divides it into two halves. As each of these halves has three sides, each half is a triangle.

• A quadrilateral is characterized with four vertices

The Angles of A Quadrilateral.

The angle of a quadrilateral refers to the angular distance between any two adjacent sides of the quadrilateral, measured in degrees or radians.

The following is important information regarding the angles of a quadrilateral.

• There are four interior angles in any quadrilateral.

• There are four exterior angles in a quadrilateral.

• Every quadrilateral has two pairs of opposite angles.

• The sum of all the interior angles of every quadrilateral is equal to 360 degrees or two times π radians

The Types of A Quadrilateral.

The following are some of the types of quadrilaterals.

• Parallelogram

• Trapezium

• Rectangle

• Square

• Rhombus

• Cyclic Quadrilateral

• Acyclic Quadrilateral

Conclusion

• The quadrilateral with its opposite sides parallel and equal to each other is termed as a parallelogram.

• A rectangle is a quadrilateral with all its interior angles equal to 90 degrees or π/2 radians.

• A square is a type of quadrilateral which has equal sides and each of its interior angles is a right angle.

• A rhombus is a variety of quadrilaterals which has equal sides, opposite sides are parallel and opposite angles are equal

• The quadrilateral with only one pair of opposite sides parallel to each other is a trapezium.

• The sum of all the angles of any quadrilateral is equal to the sum of four right angles.

• The sum of opposite angles of a cyclic quadrilateral is equal to two right angles.