+0  
 
0
6
1
avatar+328 

The number of sides of each interior angle of a regular polygon is 36 less than 8 times the measure of each exterior angle. Find the number of sides of the polygon.

 Jan 26, 2024
 #1
avatar+259 
0

Let n be the number of sides of the polygon, and let x be the measure of each exterior angle in degrees. We are given that:

 

Each interior angle is 36 less than 8 times the measure of each exterior angle: 180−n⋅x=8x−36

 

The sum of the interior angles of a polygon is (n−2)⋅180 degrees.

 

Using the first equation:

 

Solve the first equation for x: 9x=216⇒x=24

 

Substitute this value of x back into the first equation: 180−n⋅24=192−36 ⇒ n⋅24=144 ⇒ n=6​

 

Therefore, the polygon has six sides.

 Feb 11, 2024

4 Online Users

avatar