A quadrulatera is made up of four lines.

Consider a quadrilateral PQRS.

Join QS.

To prove: ∠P + ∠Q + ∠R + ∠S = 360º

Proof:

Consider triangle PQS, we have,

=> ∠P + ∠PQS + ∠PSQ = 180º ... 1  [Using Angle sum property of Triangle]

Similarly, in triangle QRS, we have,

=> ∠SQR + ∠R + ∠QSR = 180º ... 2  [Using Angle sum property of Triangle]

On adding 1 and 2, we get

∠P + ∠PQS + ∠PSQ + ∠SQR + ∠R + ∠QSR = 180º + 180º

=> ∠P + ∠PQS + ∠SQR + ∠R + ∠QSR + ∠PSQ  = 360º

=> ∠P + ∠Q + ∠R + ∠S  = 360º

Hence, the sum of angles of quadrilaterals is equal to 360 degrees