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sum of angle of quadrilateral is 360 dgree

Asked by yash 10th October 2013, 6:34 PM
Answered by Expert
Answer:

Consider a quadrilateral PQRS.

Join QS.

To prove: ?P + ?Q + ?R + ?S = 360

Proof:

Consider triangle PQS, we have,

? ?P + ?PQS + ?PSQ = 180 ... (1) [Using Angle sum property of Triangle]

Similarly, in triangle QRS, we have,

? ?SQR + ?R + ?QSR = 180 ... (2) [Using Angle sum property of Triangle]

On adding (1) and (2), we get

?P + ?PQS + ?PSQ + ?SQR + ?R + ?QSR = 180 + 180

? ?P + ?PQS + ?SQR + ?R + ?QSR + ?PSQ = 360

? ?P + ?Q + ?R + ?S = 360 [Hence proved]

Answered by Expert 10th October 2013, 9:25 PM
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