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Question

In a triangle ABC, M is the mid-point of BC. If AMB = 45, and ACM = 30, then BAM is (B is not obtuse)
  1. 30˚
  2. 45˚
  3. < 30˚
  4. ≥ 45˚


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).

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