It All Came From Pencils 3

We can make "pencilogons" by aligning multiple, identical pencils end-of-tip to start-of-tip together without leaving any gaps, as shown above, so that the enclosed area forms a regular polygon (the example above left is an 8-pencilogon).

Hazri wants to make an nn-pencilogon using nn identical pencils with pencil tips of angle 7.7^\circ. After he aligns n18n-18 pencils, he finds out the gap between the two ends is too small to fit in another pencil.

So, in order to complete the pencilogon, he has to sharpen all the nn pencils so that the angle of all the pencil tips becomes (7m)(7-m)^\circ.

Find the value of m+nm+n.

(Assume the pencils have a rectangular body and have their tips resembling isosceles triangles)


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