17) A leather ball is obtained by sewing 20 pieces of leather in the shape of hexagons and 12 pieces of leather in the shape of pentagons. A seam joins the sides of two adjacent pieces. Then the total number of seams is
$\begin{array}{ll}\text { (A) } 90 & \text { (B) } 172\end{array}$
(C) 176
(D) 180
(E) the data in the problem are insufficient.

![](https://cdn.mathpix.com/cropped/2024_04_17_58bef2a2a14f9f84b61bg-2.jpg?height=276&width=284&top_left_y=131&top_left_x=2491)
17) The answer is $(\mathbf{A})$.

Indeed, by counting the number of seams adjacent to the hexagons $(6 \cdot 20=120)$, plus the number of seams adjacent to the pentagons $(5 \cdot 12=60)$ and noting that each seam is counted twice (because it is adjacent to two polygons), we get $\frac{120+60}{2}=90$.