What is the measure of each interior angle in a regular 24-gon? i'll fan!
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We know that the interior angles in a triangle measures 180 degrees.You can divide your polygon into smaller triangles, By drawing one of the diagonals in a 4-sided figure, you have made it into 2 triangles. Each triangle measures 180 degrees so a quadrilaterals interior angles have a sum of 360 degrees. A pentagon (5-sided polygon) can be divided into 3 triangles, 6-sided into 4 triangles, 7-sided into 5 triangles, 8-sided into 6 triangles, etc. Notice that the number of triangles a polygon can be divided into is always 2 less than the number of sides. So a 24-sided polygon can be divided into 22 triangles. If each triangles interior angles measures 180 degrees then 22 triangles would measure 22 times 180 degrees for a total of 3960 degrees.
The number of angles equals the number of sides so there are 3960 degrees divided equally among 24 angles for 165 degrees for each angle.