The measure of an interior angle of a regular polygon is 135 degrees. Find the number of sides in the polygon. This is what I tried:
180(x-2)=135 [Interior Angle Sum Theorem]
x-2=.75
x=2.75
That can't be right though. Help?
Not sure about your formula.
Number of sides = 360/(180-interior angle)
so
Number of sides = 360/(180-135)
= 360/45
= 8
180(x-2) gives you the SUM of the interior angles, so each angle would be 180(x-2)/x
your equation would be
180(x-2)/x = 135
Sove it, you will get the answer DrRuss got.
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I don't get it
To find the number of sides in a regular polygon when given the measure of an interior angle, you can use the formula:
Number of sides = 360 degrees / (180 degrees - measure of interior angle)
In this case, the measure of the interior angle is 135 degrees. Plugging it into the formula, we get:
Number of sides = 360 degrees / (180 degrees - 135 degrees)
= 360 degrees / 45 degrees
= 8
Therefore, the number of sides in the polygon is 8.
The equation you attempted to use, 180(x-2) = 135, is incorrect. This equation solves for the sum of the interior angles of any polygon, not the measure of a single angle. To find the measure of a single angle in a regular polygon, you need to divide the sum of the interior angles by the number of sides.