Question

Find the number of sides of a regular polygon, if each of its exterior angle measures 36°. Name the polygon and find the number of diagonals that can be drawn in that polygon.

Answer 1

let the exterior angle be 36°

Now the interior angle and exterior angle with the line extended add to equal to 180 degrees since the line drawn is a straight line. Therefore, if one exterior angle of the regular polygon is 36, then the interior angle is

$180 - 36 = 144$

The angle sum of any polygon is given by

$180(n - 2)$

where n is the number of sides of the polygon.

So, the number of the sides =

$180(n - 2) = 144n \\ = > 180n - 360 = 144n \\ = > 36n \: = 360 \\ = > n = 10$

Since, the number of the polygon is 10 and it must be decagon.

And the diagonal of decagon is 35.