Let the circles $k_1$ and $k_2$ intersect at two points $A$ and $B$, and let $t$ be a common tangent of $k_1$ and $k_2$ that touches $k_1$ and $k_2$ at $M$ and $N$ respectively. If $t\perp AM$ and $MN=2AM$, evaluate the angle $NMB$. The original answer is in the format of an angle in degrees. Please provide the integer part of the degrees measure.

Let's think step by step and output the final answer within \boxed{}.
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