In the given figure, ∠ABC=69∘ and ∠ACB=31∘. Find ∠BDC.
A
60∘
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B
70∘
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C
100∘
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D
80∘
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Solution
The correct option is D80∘ Given that ∠ABC=69∘ and ∠ACB=31∘. Using angle sum property in △ABC, we have ∠BAC+∠ABC+∠ACB=180∘. i.e., ∠BAC+69∘+31∘=180∘ ⟹∠BAC=180∘−100∘=80∘ Now, since the angles in the same segment are equal, ∠BAC=∠BDC. ∴∠BDC=80∘