Question

show that all the Angles of quadrilateral is 360

Answer 1

first make a quad using paper curring and pasting cut angles and join them you will form a circle

Answer 2

Consider a quadrilateral PQRS.
Join QS.
To prove: ∠P + ∠Q + ∠R + ∠S = 360°
Proof:

Consider triangle PQS, we have,
⇒∠P + ∠PQS + ∠PSQ = 180°......(1) [Angle sum property of triangle]

Similarly in triangle QRS we have,
⇒∠SQR + ∠R + ∠QSR = 180°.......(2) [Angle sum property of triangle]

On adding (1) and (2) we get:
∠P + ∠PQS + ∠PSQ + ∠SQR + ∠R + ∠QSR = 180° + 180°
∠P + ∠PQS + ∠PSQ + ∠SQR + ∠R + ∠QSR = 360°
[Hence Proved] ∠P + ∠Q + ∠R + ∠S = 360°