If the measure of each of the interior angles of a polygon is $108 °$ , then find the number of sides of the regular polygon.

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Solution

The measure of each of the interior angles of any polygons having number of sides $n$ is given by $= \frac{(n - 2) \times 180 °}{n}$
So,
$\frac{(n - 2) \times 180 °}{n} = 108 ° 180 n - 360 = 108 n 72 n = 360 n = 5$
Hence, the number of sides = $5$

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If the measure of each of the interior angles of a polygon is 108°, then find the number of sides of the regular polygon.

The measure of each of the interior angles of any polygons having number of sides n is given by =(n-2)×180°nSo, (n-2)×180°n=108°180n-360=108n72n=360n=5Hence, the number of sides = 5

If the measure of each of the interior angles of a polygon is $108 °$ , then find the number of sides of the regular polygon.

The measure of each of the interior angles of any polygons having number of sides $n$ is given by $= \frac{(n - 2) \times 180 °}{n}$
So,
$\frac{(n - 2) \times 180 °}{n} = 108 ° 180 n - 360 = 108 n 72 n = 360 n = 5$
Hence, the number of sides = $5$