Final answer:
The number of vertices in the planar Eulerian graph is 10 and the number of edges is 21.
Step-by-step explanation:
An Eulerian graph is a graph that contains a closed trail that includes every edge exactly once. In a planar Eulerian graph, the closed trail does not intersect itself.
In a planar Eulerian graph, the number of vertices (V), edges (E), and faces (F) are related by the formula V + F = E + 2. Since the graph in question has 10 vertices and 21 edges, we can calculate the number of faces using the formula: F = E + 2 - V = 21 + 2 - 10 = 13.
Therefore, the number of vertices in the planar Eulerian graph is 10 and the number of edges is 21.