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Prove that..... The four angles of …

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Prove that..... The four angles of the quadrilateral is 360.

Posted by Piyush Gautam 8 years, 3 months ago

CBSE > Class 09 > Mathematics

2 answers

Golua Singham 8 years, 3 months ago

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°. Angle Sum Property of a Quadrilateral 0Save Therefore, 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°.

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Ramu Kevat 8 years, 3 months ago

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