Exterior angle of a regular polygon measures #10alpha# degrees.Then, prove that #alpha in ZZ# and there are precisely 7 such alpha#?

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Answer 1 · 2018-07-18T01:36:00

We know, the magnitude of each external angle of a regular polygon of #n# sides is related as follows.

Each external angle (#theta#) #=360^@/n#,where n must be an positive integer #>=3#.

Now it is given #theta=10alpha# degree

So #10alpha=360^@/n#

#=>alpha=36/n#

This shows that possible positive integral values of #alpha# are 12,9,6,4,3,2,1.

Hence #alpha inZZ# takes precisely 7 values.