Why do all exterior angles on a polygon add up to 360 when the interior changes depending on sides?
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Idk if you have ever used the program MS logo, but imagine you are on a giant piece of paper and that you are drawing with your feet (like a turtle in said program).
When you make a regular polygon you are going to move some distance forward and some angle to the left (or right, but let’s keep it counter clockwise for simplicity). Then you move forward and repeat this process till you are back at the starting position (If you are back to where you started, you created a regular polygon, else it’s just a random shape).
Let’s recreate this motion that you used to create said polygon. The only difference this time is that you do not move forward but only turn. After the first step you have turned some angle, and so on and on. On the last step, you turn one final angle and are facing the original position, i.e. you turned 360°. This means that the sun of all left turns is 360.
By virtue of turning left to create the polygon, the angle you turned is the exterior angle of the polygon. Hence through this thought experiment (I think it’s called the spider problem) we have demonstrated that no matter the polygon, the sum of exterior angle is ALWAYS a full rotation (360°).
By basic geometry the interior angle is (180° – exterior angle). And the number of internal angles created is dependent on the number of polygonal sides you created ie the number of steps you took in this experiment. Hence it depends on the polygon.
Please lmk if you need elaboration
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