7. A polygon is said to be convex if all its internal angles have a strictly smaller measure than $180^{\circ}$. What is the maximum number of angles with a measure less than $150^{\circ}$ that a convex polygon with 2016 sides can have?
(A) 11
(B) 12
(C) 13
(D) 17
(E) 2016
7. The answer is (A). Consider a convex polygon with 2016 sides, and suppose it has exactly $a$ angles with a measure less than $150^{\circ}$; the sum of its interior angles is (2016 2) $180^{\circ}$. At the same time, since each of the 2016 - $a$ remaining angles has a measure less than $180^{\circ}$, this sum is strictly less than $a \cdot 150^{\circ}+(2016-a) \cdot 180^{\circ}$. We thus obtain the inequality

$$
2014 \cdot 180^{\circ}<a \cdot 150^{\circ}+(2016-a) \cdot 180^{\circ} \text {, }
$$

or $a \cdot 30^{\circ}<360^{\circ}$, from which $a<12$.

On the other hand, it is not difficult to see that there exists a polygon with 11 angles of measure $149^{\circ}$ and 2005 angles of measure $\frac{1}{2005}\left(2014 \cdot 180^{\circ}-11 \cdot 149^{\circ}\right)$.