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In a regular polygon, there are two diagonals intersect inside the polygon at an angle of $$50^\circ$$. The least number of sides of the polygon for which this is possible is
An angle formed by two intersecting diagonals of a regular $$n$$-gon is an integer multiple of $$\frac{180^\circ}{n}$$. Thus $$50^\circ=k\frac{180^\circ}{n}$$ for some positive integer $$k$$, so $$5n=18k$$. The least possible $$n$$ is therefore $$18$$, and suitable diagonals can be chosen to produce the required angle.
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