SOLUTION: can you please help me solve: (((A regular polygon has 12 sides. Find the measure of each interior angle.)))

Question 182680This question is from textbook Geometry
: can you please help me solve: (((A regular polygon has 12 sides. Find the measure of each interior angle.))) This question is from textbook Geometry

Answer by J2R2R(94) (Show Source): You can put this solution on YOUR website!
For all polygons, the sum of all exterior angles adds up to 360 degrees. For each vertex, the interior angle plus the exterior angle = 180 degrees, so if a regular pentagon has 12 sides, then for all 12 exterior angles to add up to 360 degrees each one must be 30 degrees.

Therefore the interior angle is 180 degrees minus 30 degrees = 150 degrees.

Hint:

This might help you see how this works.

Draw a regular polygon with a circle passing through all vertices. Join the centre to each vertex and use geometry to reason that for each side of the polygon, the angle subtended at the centre of the circle of the triangle formed from both ends of the side to the centre of the circle equals the exterior angle. You only have to do this once since it applies equally to all sides.

As the angles at the centre represent the exterior angles and altogether make a circle (360 degrees) then the sum of all exterior angles is 360 degrees and this applies irrespective of whether it is a regular polygon or not.

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