Prove that the sum of four angles of a quadrilateral is 360 degrees.
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In a quadrilateral ABCD,join BD . since the sum of the angles of a triangle is 180°
therefore
In ∆ABD, we have <1 + <A + <2 = 180° ....(1)
In ∆ABC,we have <3 + <C + <4 = 180° ....(2)
Adding (1 ) and (2), we get
[<1 + <A + <2] + [<3 + <C + <4]= 180° + 180°
(<1 + <3) + <A+<C + (<2+<4)= 180° + 180°
so, <A+<B+<C+<D= 360°
Therefore the sum of four angles of a quadrilateral is 360°
therefore
In ∆ABD, we have <1 + <A + <2 = 180° ....(1)
In ∆ABC,we have <3 + <C + <4 = 180° ....(2)
Adding (1 ) and (2), we get
[<1 + <A + <2] + [<3 + <C + <4]= 180° + 180°
(<1 + <3) + <A+<C + (<2+<4)= 180° + 180°
so, <A+<B+<C+<D= 360°
Therefore the sum of four angles of a quadrilateral is 360°
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