How many will a regular polygon have if the measure of each angle is 165 degree?

Recall that 180(n-2) = total measure of all interior angle
And each interior angle = [(180(n-2)]/n
where n = number of sides


So rewrite the equation: n(measure interior angle) = (180)(n-2)

Substituting:
(165)n = (180)(n - 2)
360 = 15 n
n = 24

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