SOLUTION: The measure of each interior angle of a regular polygon is 24 more than 38 times the measure of each exterior angle. Find the number of sides of the polygon.
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-> SOLUTION: The measure of each interior angle of a regular polygon is 24 more than 38 times the measure of each exterior angle. Find the number of sides of the polygon.
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Question 1102475: The measure of each interior angle of a regular polygon is 24 more than 38 times the measure of each exterior angle. Find the number of sides of the polygon.
I attempted this by trying to solve for each interior angle.
I+24=38E and got I=178
Then, I entered that in [180(n-2)]/n =178. I got 180 and the answer should be 90. Where did I go wrong? Found 2 solutions by Alan3354, KMST:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The measure of each interior angle of a regular polygon is 24 more than 38 times the measure of each exterior angle. Find the number of sides of the polygon.
I attempted this by trying to solve for each interior angle.
I+24=38E and got I=178
Then, I entered that in [180(n-2)]/n =178. I got 180 and the answer should be 90. Where did I go wrong?
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Int + Ext = 180
I = 38E + 24
--> 38E + 24 + E = 180
39E = 156
E = 4 degs
sides = 360/E = 90 sides
You can put this solution on YOUR website! If = measure of each exterior angle, and = measure of each interior angle,
then = 38 times the measure of each exterior angle, and = 24 more than 38 times the measure of each exterior angle.
So, your equation should have been .
I do not know how you got from ,
but it is often easier to work with exterior angles,
because is much easier to remember and use
than the unwieldy .
