Question

Find the measure of each interior angle of a regular 18 sided polygon​

Answer 1

The formula that gives the measure of the interior angle of a regular polygon is: (n-2)*180/n, where n is the number of sides. The measure of one angle of the regular polygon whose number of sides is 18, is of 160 degrees.

Answer 2

The measure of each interior angle of a regular 18 sided polygon is 160°

Given :

A polygon with 18 sides

To find :

The measure of each interior angle

Formula :

The sum of interior angles of a polygon with n sides = ( n - 2 ) × 180°

Solution :

Step 1 of 3 :

Write down the number of sides

Here it is given that the polygon has 18 sides

Step 2 of 3 :

Find sum of interior angles of a polygon

Number of sides = n = 18

The sum of interior angles of the polygon

= ( 18 - 2 ) × 180°

= 16 × 180°

= 2880°

Step 3 of 3 :

Measure each interior angle

Number of sides = n = 18

The sum of interior angles of the polygon = 2880°

The measure of each interior angle

$\displaystyle \sf{ = \frac{ {2880}^{ \circ}}{18} }$

$\sf = {160}^{ \circ}$

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