1.

How many sides does a regular polygon have if each of its interior angles is `165^@` ?

Answer» Let number of sides of given regular polygon is `n`.
Then, sum of all of the angles can be given as,
`S = (n-2)**180^@->(1)`
Also, as we are given each interior angle is `165^@`,
So, Sum of all the angles will also be,
`S = 165n->(2)`
From (1) and (2),
`(n-2)**180 = 165n`
`180n - 360 = 165n => 15n = 360 => n = 360/15 = 24`
So, number of sides in the given polygon is `24`.


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