Find the number of sides of a regular polygon, when each of its angles has a measure of $135^{o}$

8

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Solution

The correct option is B $8$
Each interior angle of a regular polygon = $\frac{180^{o} (n - 2)}{n}$ where n = number of sides of polygon.
Given, each of its angles has a measure of $135^{o}$ .
$\frac{180^{o} (n - 2)}{n} = 135^{o}$
$=> 180^{o} n - 135^{o} n = 360^{o}$
$=> 45^{o} n = 360^{o}$
$=> n = 8$

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Find the number of sides of a regular polygon, when each of its angles has a measure of 135o

The correct option is B 8Each interior angle of a regular polygon = 180o(n−2)n where n = number of sides of polygon.Given, each of its angles has a measure of 135o.180o(n−2)n=135o=>180on−135on=360o=>45on=360o=>n=8

Find the number of sides of a regular polygon, when each of its angles has a measure of $135^{o}$