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To solve this problem, let's analyze the information given:

1. You're dealing with a triangle \( \triangle ABC \) where the bisectors of angles \( A \) and \( B \) intersect at a point \( M \).
2. You're given that \( \angle C = 160^\circ \).
3. You need to find \( \angle AMB \).

To find \( \angle AMB \), we can use the following property of triangle angle bisectors:

The angle between the bisectors of angles \( A \) and \( B \) in a triangle is equal to \( 90^\circ + \frac{C}{2} \), where \( C \) is the angle opposite the side where the bisectors are meeting.

Let's calculate it:

1. \( C = 160^\circ \).
2. \( \angle AMB = 90^\circ + \frac{160^\circ}{2} \).
3. \( \angle AMB = 90^\circ + 80^\circ = 170^\circ \).

Therefore, the answer is \( 170 \).