A regular polygon has 24 sides. What is the measure of each interior angle?

Question

Please help me because Geometry is soooooooo  hard!!!!!!!!!!

Answer 1

In the 1960's, Seymour Papert and his team at M.I.T. invented a computer-controlled "turtle" that could draw on paper on the floor.  Turtle Graphics is still a great way to explore Geometry. 

 

If a turtle starts facing East and turns and turns and turns and ... turns and ends up at the starting point facing in the same direction as when it started, it has turned 360°.  In Geometry, we say, "The sum of the external angles is 360°."

 

Now, a 24-sided regular polygon has 24 turns, each with an external angle of 360°/24, right?

 

And, each interior angle is 180° - (360°/24) because the turtle doesn't go back the way it came, but it turns a angle that is the supplement of the exterior angle  ["Two angles are supplementary if their angles add up to 180".]

 

Thus, there is a formula for the internal angle of a regular n-sided polygon:

 

                180° - 360°/n

 

                (n-2)*180°/n

Answer 2

Use the formula for the measure of each interior angle of a regular polygon.

a = [(180(n-2)]/n

a = [(180(24-2)]/24

a = 3960/24

a = 165º

Answer 3

To find the measure of an interior angle of a regular polygon, take the sum of all interior angles and divide by the number of angles.

 

The sum of all interior angles can be found by (n - 2)*180 where n is the number of sides, in this case 24.

 

(24-2)*180 = 3960

 

So all the interior angles add to 3960 degrees.

 

To find each angle take that sum and divide by the number of angles, 24 to get that each interior angle is 165 degrees