19.5 The six interior angles of a convex hexagon form an arithmetic sequence of natural numbers. Let $m^{\circ}$ be the measure of the largest angle of this hexagon, then the maximum possible value of $m^{\circ}$ is
(A) $165^{\circ}$.
(B) $167^{\circ}$.
(C) $170^{\circ}$.
(D) $175^{\circ}$.
(E) $179^{\circ}$.
(42nd American High School Mathematics Examination, 1991)
［Solution］Let the common difference of the arithmetic sequence be $d^{\circ}$, according to the problem, we have
$$
6 m-\frac{6(6-1)}{2} d=(6-2) \cdot 180,
$$

which simplifies to $6 m-15 d=720$, or $m=120+\frac{5 d}{2}$.
Therefore, $m=120+\frac{5 d}{2}<180^{\circ}$, which implies $d<24$. Since $m$ is a natural number, $d$ must be even, so $d=22$. Thus,
$$
m=120+\frac{5 \cdot 22}{2}=175 \text {. }
$$

Hence, the answer is $(D)$.