sum of angle of quadrilateral is 360 dgree

Asked by yash | 10th Oct, 2013, 06:34: PM

Expert Answer:

Consider a quadrilateral PQRS.

Join QS.

To prove: ?P + ?Q + ?R + ?S = 360º

Proof:

Consider triangle PQS, we have,

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

Similarly, in triangle QRS, we have,

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

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

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

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

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

Answered by  | 10th Oct, 2013, 09:25: PM

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