Prove that the sum of all the angles of a quadrilateral is 360 degree

(Hint: The sum of the angles in a triangle is 180 degree)

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 proved]