Question

prove the sum of four angles in quadrilateral is 360 degree​

Answer 1

Answer:

this is your Answer hope it helps you

Step-by-step explanation:

Consider a quad quadrilateral ABCD.

Join QS.

To\quad prove:∠A+∠B+∠C+∠D=360º

Proof:Consider triangle ABD,

we have,∠A+∠ABD+∠ADB=180º⟹(1)[Using Angle sum property of Triangle]

Similarly,triangle BCD,we have,∠DBC+∠C+∠BDC=180º⟹(2)[Using Angle sum property of Triangle]

On adding (1) and (2),we get∠A+∠ABD+∠ADB+∠DBC+∠C+∠BDC=180º+180º

∠A+∠B+∠C+∠D=360º

Answer 2

Consider a quadrilateral PQRS

Join QS

To Prove :angle P +angle Q +angle R + angle S =360°

Proof: Consider triangle PQS ,we have,

•angle P +angle PQS + angle PSQ=180°....(1)(ASP OF TRIANGLE)

Similarly, in triangle QRS,we have,

•angle SQR + angle R + angle QSR=180°...(2)(ASP OF TRIANGLE)

By adding (1)&(2),we get,

angle P+angle PQS + angle PSQ + angle SQR + angle R + angle QSR=180°+180°

●angle P + angle PQS + angle SQR +angle R +angle PSQ=360°

●angle P +angle Q + angle R + angle S =360°