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sum of the exterior angle of a triangle is 180
therefore angle ACD +angleBAE +angleCBF =180
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∠abc+∠bac+∠acb=180(angle sum property) ------1 e
∠abc+∠cbf=180(linear pair)
∠abc=180-∠cbf
similarly,
∠bac=180-∠bae
∠acb=180-∠acd
now substituting these values in the first eqn
180-∠cbf+180-∠bae+180-∠acd=180
180+180+180-∠cbf-∠bae-∠acd=180
180+180+180-180=∠cbf+∠bae+∠acd
∠cbf+∠bae+∠acd=180+180
∠cbf+∠bae+∠acd=360
hence proved
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