show that sum of four angles of a quadrilateral is 360
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Answer:
We know that the sum of the angles of a triangle is 180°. ⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)]. Hence, the sum of all the four angles of a quadrilateral is 360°.
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Step-by-step explanation:
Consider a quadrilateral PQRS, QS is the diagonal.
To prove : ∠P + ∠Q + ∠R + ∠S = 360º
Proof:
In triangle PQS, we have,
∠P + ∠PQS + ∠PSQ = 180º ... (i) [Using Angle sum property of Triangle]
Similarly, in triangle QRS, we have,
∠SQR + ∠R + ∠QSR = 180º ... (ii) [Using Angle sum property of Triangle]
Adding (i) and (ii), we get ,
∠P + ∠PQS + ∠PSQ + ∠SQR + ∠R + ∠QSR = 180º + 180º
⇒ ∠P + ∠PQS + ∠SQR + ∠R + ∠QSR + ∠PSQ = 360º
Also, ∠PQS + ∠SQR = ∠PQR and ∠QSR + ∠PSQ = ∠PSR
⇒ ∠P + ∠Q + ∠R + ∠S = 360º
Hence proved
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