About Angle Sum Property of a Quadrilateral

Let’s look at some terms and conventions related to quadrilaterals before understanding the Angle Sum Property of Quadrilateral:

Opposite Sides: Two Sides of the quadrilateral are called opposite sides if they have no common vertex. 

For example: In the figure given above look at the quad ABCD. Here, AB and CD are opposite sides. Similarly, AD and BC are opposite sides. 

Opposite Angles: Two angles of a quadrilateral are opposite if they don’t have any common arm. 

For example: In the figure ABCD again, angle A and angle C don’t have any common arm. Thus, they can be considered as opposite angles. Similarly, angles B and D are also opposite angles. 

Adjacent Sides: Two sides are called adjacent if sides have a common vertex.

For example: AB and AD have common vertex “A”. So, they are called adjacent sides. Similarly, AB, BC; BC, CD and AD, DC are adjacent sides.  

Adjacent Angles: Two angles, if they have a common arm are called adjacent angles. 

For example: ∠A, ∠B are adjacent angles. 

Example: List the pair of opposite sides and adjacent angles from the quadrilateral given below. 

Solution: 

Pair of opposite sides are the sides which don’t have any common vertices. 

So, in this case (AB, CD) and (AC, BD) are two pairs of opposite sides. 

Similarly, going by the definition given above. Pair of adjacent sides are, 

(AC, AB); (AB, BD); (BD, DC); (CD, AC)  

Angle Sum Property of a Quadrilateral: Quadrilaterals are encountered everywhere in life, every square rectangle, any shape with four sides is a quadrilateral. We know, three non-collinear points make a triangle. Similarly, four non-collinear points take up a shape that is called a quadrilateral. It has four sides, four angles, and four vertices. 

Both the figures above are examples of quadrilaterals. ABCD is a quadrilateral. AB, BC, CD, and DA are the four sides of the quadrilateral. A, B, C, and D are four vertices, and ∠A, ∠B, ∠C, and ∠D are the angles of this quadrilateral. Before coming to the Angle Sum Property of Quadrilateral we have to know some basic terminologies of quadrilateral, which are discussed below in the article.