【Question 15】
Suppose there is a convex polygon, and the sum of all other interior angles except one is $2015^{\circ}$. Try to find the degree measure of this interior angle.
【Analysis and Solution】
Geometry, angles.
Since this is a convex polygon;
each interior angle is less than $180^{\circ}$;
because the sum of all other interior angles except one is $2015^{\circ}$;
the sum of the interior angles of this polygon is greater than $2015^{\circ}$ and less than $2015^{\circ}+180^{\circ}=2195^{\circ}$; and the sum of the interior angles of a polygon is an integer multiple of $180^{\circ}$;
$$
2015 \div 180=11 \cdots \cdots 35,2195 \div 180=12 \cdots \cdots 35 \text {; }
$$

Therefore, the sum of the interior angles of this polygon is $12 \times 180^{\circ}=2160^{\circ}$;
the removed interior angle is $2160^{\circ}-2015^{\circ}=145^{\circ}$.