What is the measure of each interior angle of an 18 sided polygon?

Question

107288 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-05T22:05:00

$160°$

An alternative method is to use the exterior angle.

enter image source here
the sum of the exterior angles is ALWAYS $360°$

So you can find the size of the exterior angles of a regular polygon quite easily:

If there are $18$ sides $(n=18)$ , then each exterior angle is:

$(360°)/n = (360°)/18 = 20°$

The sum of the exterior and interior angles is $180°$ because they are adjacent angles on a straight line.

$:.$ each interior angle is $180° - 20° = 160°$

Answer 2 · 2018-03-03T04:53:17

Each interior angle of an 18 sided polygon is $color(brown)(160^@)$

enter image source here

Sum of the interior angles of a polygon is given by the formula

$n * I_18 = (2n - 4) * 90^@ or = (n - 2) * 180^@$

Since it’s an 18 sided polygon, $n = 18$

Therefore $hat I_18 = ((18-2) * cancel(180)^color(brown)(10)) / cancel18 = (16 * 10 )= 160^@$