Question

prove that some of the angles of a quadrilateral is 360 degree????​

Answer 1

$\text{Consider a quadrilateral PQRS.}\\\\\text{Join QS.}\\\\\text{To prove: \angle P + \angle Q + \angle R + \angle S = 360^{\circ} }$

$\text{Proof:}\\\\\text{Consider triangle PQS, we have,}\\\\\text{ \implies \angle P + \angle PQS + \angle PSQ = 180 ^{\circ} ... (1) [Using Angle sum property of Triangle]}$

$\text{Similarly, in triangle QRS, we have,}\\\\\text{ \implies \angle SQR + \angle R + \angle QSR = 180 ^{\circ} ... (2) [Using Angle sum property of Triangle]}\\\\\text{On adding (1) and (2), we get}\\\\\text{ \angle P + \angle PQS + \angle PSQ + \angle SQR + \angle R + \angle QSR = 180 ^{\circ} + 180 ^{\circ} }\\\\\text{ \imples \angle P + \angle PQS + \angle SQR + \angle R + \angle QSR + \angle PSQ = 360 ^{\circ} }$

$\text{ \implies \angle P + \angle Q + \angle R + \angle S = 360 ^{\circ} }\\\\\text{Hence, proved}$