Prove the exterior angle property of quadrilateral​

Question

Prove the exterior angle property of quadrilateral​

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Clara 1 month 2021-10-27T01:58:03+00:00 2 Answers 0 views 0

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    0
    2021-10-27T01:59:37+00:00

    Answer:

    Step-by-step explanation: 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



    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°.

    0
    2021-10-27T02:00:01+00:00

    Answer:

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