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]

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