: The interior angles of a convex hexagon are all positive integers and form an arithmetic sequence, with the largest angle being $a$ degrees. Then the maximum value of $a$ is
(A) $165^{\circ}$
(B) $167^{\circ}$
(C) $170^{\circ}$
(D) $175^{\circ}$
3. (I)).

From the problem, we know that $a-5d, a-4d, a \cdots-3d, a-2d, a-d, a$ are the interior angles of a hexagon, so $(a-5d) + (a-4d) + \cdots + a = 6a - 15d$.

Also, $6a - 15d = (6-2) \times 180 = 4 \times 180$. Thus, $2a = 5d + 240$, and $d$ is an even number. Given $0 < a < 180$, we have $5d + 240 < 360$, which gives $d < 24$. Therefore, the maximum value of $d$ is 22, and thus the maximum value of $a$ is $(5 \times 22 + 240) \div 2 = 175$.