Question

In a triangle ABC, M is the mid-point of BC. If $\angle$AMB = 45${}^{\circ }$, and $\angle$ACM = 30${}^{\circ }$, then $\angle$BAM is ($\angle$B is not obtuse)

• A. 30˚
• B. 45˚
• C. < 30˚
• D. ≥ 45˚

Answer 1

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 angles. Hence DAM = 45 and BAM > 45. BAM= 45${}^{\circ }$ If $\angle$ABC =90${}^{\circ }$. hence, answer is option (d)