There are a total of 35 triangles

How?
Lets count the number of triangles where side of the pentagon is one of the side of the triangle, for each one such side there are 6 triangles. but two of triangle has other side of the pentagon, those will be counted twice so we will count only one triangle for each side, so for five sides, total 5*5 = 25 such triangles.

Now, lets count the triangles where side of the pentagon is not the side of the triangle: there are 5+5 = 10 such triangles, this will be clear by the below diagram(5 green and 5 red triangles).

how many triangles in this pentagon answer

Thus, there are a total of 25+ 10= 35 triangles

There are a total of 84 triangles

How?
Lets count…
Looking at the symmetry, we can divide this triangle in 4 equal parts(square) and we will first count the number of triangles in each part and then number of triangles formed by combining 2 or more parts together.
Number of triangles in one square: 8(non overlapping triangles) + 4(overlapping triangles with middle lines a part of the triangle) =12
Number of triangles by taking two squares at a time: 6(try a little harder, you will fidn these) * 4(there are four such combinations) = 24
Number of triangles by taking (only) three squares at a time: 1(all squares should be a part of the triangle) *4(four such combinations) = 4
Number of triangles by taking all squares together = 8

Thus total number of triangles = 12*4 + 24 + 4 + 8 = 84.