In a triangle ABC, M is the mid-point of BC. If ∠AMB = 45∘, and ∠ACM = 30∘, then ∠BAM is (∠B is not obtuse)
A
30˚
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B
45˚
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C
< 30˚
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D
≥ 45˚
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Solution
The correct option is D ≥ 45˚ Consider any triangle ABC, AM is a line connecting A to mid point of BC. Drop a perpendicular from A to BC touching BC at D. The angle ADM is a right-angled triangle with 45∘ – 45∘ – 90∘ . Hence DAM = 45∘ and BAM > 45∘ . BAM= 45∘ if ∠ABC =90∘. Hence, answer is option (d).