Question

Prove that the sum of 4 angles of a quadrilayeral is 360

Answer 1

Answer:

please mark as briliant answer

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Proof: Let ABCD be a quadrilateral. Join AC. Clearly, ∠1 + ∠2 = ∠A ...... (i) And, ∠3 + ∠4 = ∠C ...... (ii) We know that the sum of the angles of a triangle is 180°.0SaveTherefore, from ∆ABC, we have∠2 + ∠4 + ∠B = 180° (Angle sum property of triangle) From ∆ACD, we have ∠1 + ∠3 + ∠D = 180° (Angle sum property of triangle) Adding the angles on either side, we get; ∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 360° ⇒ (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360° ⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)]. Hence, the sum of all the four angles of a quadrilateral is 360°.