In the below given figure, prove that $∠ B D C = ∠ A + ∠ B + ∠ C$

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Solution

$∠ B D M (e x t e r i o r a n g l e) = ∠ B + ∠ B A D$

$= ∠ C D M (e x t e r i o r a n g l e) = ∠ C + ∠ C A D$

$∴ ∠ B D C = ∠ B D M + ∠ C D M$

$= ∠ B + ∠ C + (∠ B A D + ∠ C A D) = ∠ B + ∠ C + ∠ A$

$∴ ∠ B D M = ∠ B + ∠ C + ∠ A$

Hence Proved.

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