17.16 $\triangle A B C$ is an isosceles triangle with base $A C$, points $P$ and $Q$ are on $C B$ and $A B$ respectively, and $A C=A P=P Q=Q B$, then the degree measure of $\angle B$ is
(A) $25 \frac{5}{7}$.
(B) $26 \frac{1}{3}$.
(C) 30 .
(D) 40 .
(E) cannot be determined.
(12th American High School Mathematics Examination, 1961)
[Solution] Let $\angle B=x$. According to the problem and the exterior angle property of a triangle, we have $\angle Q B P=x, \angle A Q P=\angle Q A P=2 x$,

thus $\angle Q P A=180-4 x$,
then $\angle A P C=3 x, \angle A C P=3 x$.
Also, $\angle B C A=\angle B A C=3 x$, so in $\triangle A B C$, $x+3 x+3 x=180$, yielding $x=25 \frac{5}{7}$. Therefore, the answer is $(A)$.