Question

Prove the theorem the sum of the angles of a quadrilateral is 360° or 4 right angles

Answer 1

just joined the digonal of quadrilateral and applying angle sum property in both the triangles...

Answer 2

Concept: The sum of all angles of a triangle = 180°

Consider a quadrilateral PQRS

Construction: Join the diagonal QS

To prove: ∠P + ∠Q + ∠R + ∠S = 360º

Now, we shall Δ PQS and apply angle sum property of triangle.

∠P + ∠PQS + ∠PSQ = 180º --------(i)

Similarly, we shall take Δ QRS and apply angle sum property of triangle.

∠SQR + ∠R + ∠QSR = 180º -----------(ii)

Now, adding equations (i) & (ii)

∠P + ∠PQS + ∠PSQ + ∠SQR + ∠R + ∠QSR = 180º + 180º

or, ∠P + ∠PQS + ∠SQR + ∠R + ∠QSR + ∠PSQ = 360º

or, ∠P + ∠Q + ∠R + ∠S = 360º = 4×90° = 4 right angles

This is the required condition.