1.) How many triangles are there in this pentagon?
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how many triangles in this pentagon
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).
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how many triangles in this pentagon answer
Thus, there are a total of 25+ 10= 35 triangles
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I got to 30…