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

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Answer 1 · 2017-06-05T22:05:00

#160°#

An alternative method is to use the exterior angle.

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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^@) #

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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^@#