What is the value of X? Remember to show calculations and formulas used for credit. What is the measure of an exterior angle of a regular octagon? Make sure to show your calculation and formulas used for credit.
One of the rules for polygons is the sum of the exterior angles has to always be equal to 360 degrees.
Here we are dealing with a octagon of the regular kind which tells us that each angle on the inside are equal to each other. Here we will use the formula of ((s-2)*180)/s where s is the amount of sides of the shape, we will be using s=8 since it's an octagon.
((8-2)*180).8 = (6*180)/8 = 180/8 = 135 This tells us that every interior angle is equal to 135 degrees
The exterior angles are supplementary to the interior angles we will use the formula of 180 - a = b Where A is one angle and B with the supplementary angle
180 - 135 = 45
Thus the exterior angle is at 45 degrees, we could have also done this another way by just doing (360) / 8 which would also give us 45 degrees because another rule of polygons is that the sum of all exterior angles equal 360 degrees and there is 8 angles and since it's a regular octagon thus the 8 angles have to equal eatch other so 360/8 would give us just one of the exterior angles.
