Question

Prove that the sum of the angles of a quadrilateral is 360​

Answer 1

Consider PQRS as a quadrilateral, Join QS

So that we will get two triangles,

Triangle 1= PSQ and  

Triangle 2= QSR

∠P+∠PQS+∠PSQ=180° ---- (1) using angle sum property of triangle

Similarly for ORS, we have

Using sum angle property of triangle,  

Sum of all four angles of a quadrilateral will be 360°

∠SQR+∠R+∠QSR=180° ---- (2)

On adding equation 1 and 2, we get

∠P+∠PQS+∠PSQ+∠SQR+∠R+∠QSR=180°+180°  

∠P+∠Q+∠R+∠S=360°  

Sum of angles of quadrilateral is always equal to zero.

HENCE PROVED  

Answer 2

Answer:

It's as simple as that bye