Question 483998
Counting them manually is probably the easiest way to do so. Once you draw the pentagon and all its diagonals, you can find five triangles, each one having three consecutive vertices on the pentagon (e.g. V1V2V3, V2V3V4 if we label the vertices V1,...,V5). You can count six triangles in each of them, so 30 triangles. There are also five additional triangles determined by non-adjacent vertices (e.g. V1V2V4, etc.) so the answer is 35.