Question

prove that the all angles of a quadrilateral is 360

Answer 1

A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles. The sum of its interiorangles is 360 degrees

Answer 2

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