Henry Ernest Dudeney/Puzzles and Curious Problems/240 - Counting the Triangles/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $240$

Draw a pentagon, and connect each point with every other point with straight lines, as in the diagram.

How many different triangles are contained in this figure?

There are:

$5$ triangles of the form $\triangle ADC$

$5$ triangles of the form $\triangle AEB$

$5$ triangles of the form $\triangle ABF$

$5$ triangles of the form $\triangle AKF$

$10$ triangles of the form $\triangle AKB$

$5$ triangles of the form $\triangle ADG$

That seems to be all of them.

Thus there are $35$ triangles altogether.