Question

prove that the sum of all the angles of a quadrilateral is 360°

Answer 1

Here is your answer

Given:-

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]

Answer 2

Hope. useful for you