4. As shown in Figure 16, in rhombus $A B C D$, $\angle A=$ $100^{\circ}, M$ and $N$ are the midpoints of sides $A B$ and $B C$ respectively, $M P \perp C D$ at point $P$, then the degree measure of $\angle N P C$ is $\qquad$
(2007, Shandong Province Junior High School Mathematics Competition)
It is known that $\angle B=80^{\circ}$.
Notice that $B M=B N$. Then
$$
\angle B M N=\angle B N M=50^{\circ} \text {. }
$$

As shown in Figure 16, let the midpoint of $M P$ be $E$, and connect $N E$. It is easy to know that $N M=N P$. Then $\angle N M P=\angle N P M$. Therefore,
$$
\angle N P C=\angle N M B=50^{\circ} .
$$