Since this triangle is similar to the original triangle, we can set up the equation We can figure out that this triangle has a base of length 𝑥 − 1, while the legs are of length 1. This splits the triangle into two new isosceles triangles, one of which is a 72-72-36 triangle.
Then we draw the bisector to one of the 72° angles. We let the base of this isosceles triangle have length 1, and the legs have length 𝑥. The two angles you mention, 𝜋∕5 = 36° and 𝜋∕10 = 18°, we can actually find exact expressions for that aren't too complicated.
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