# It All Came From Pencils 3

Geometry Level 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 $$n$$-pencilogon using $$n$$ identical pencils with pencil tips of angle $$7^\circ.$$ After he aligns $$n-18$$ 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 $$n$$ pencils so that the angle of all the pencil tips becomes $$(7-m)^\circ$$.

Find the value of $$m+n$$.

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