Find the number of sides of a regular polygon if each of its interior angles measures $162 °$ .

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Solution

As we know that the measures of each interior angles of a polygon having $n$ sides is $= \frac{(n - 2) \times 180}{n}$
Now the measure of given interior angle is $= 162 °$
$162 ° = \frac{(n - 2) \times 180}{n} 162 n = 180 n - 360 n = \frac{360}{18} = 20$
Hence, the number of sides of a regular polygon is $20$ .

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Find the number of sides of a regular polygon if each of its interior angles measures162°.

As we know that the measures of each interior angles of a polygon having n sides is=(n−2)×180nNow the measure of given interior angle is =162°162°=(n−2)×180n162n=180n-360n=36018=20Hence, the number of sides of a regular polygon is 20.

Find the number of sides of a regular polygon if each of its interior angles measures $162 °$ .