My question is:The measure of each interior angle of a regular polygon is 8 times than of an exterior angle

The measure of each interior angle of a regular polygon is 8 times than of an exterior angle. how many sides does a polygon have?. ------------------------------ Let the measure of the exterior angle be "x" Then the measure of the interior angle is "8x" ------------- Since the two are supplementary x+8x = 180 degrees 9x = 180 x = 20 degrees (measure of each exterior angle) 8x = 160 degrees (measure of each interior angle) ------------------------------------ The sum of All of the exterior angles is 360 degrees. 360/20 = 18 (that is the number of exterior angles and says the number of sides is 18) ============================================== Cheers, Stan H.

Let I = the measure of an interior angle and E = the measure of the corresponding exterior angle. Recall that the interior angle and the exterior angle are supplementary so: I+E = 180 degrees. You are told in the problem that: I = 8E "The measure of each interior angle of a regular polygon is 8 times that of an exterior angle." Substitute I = 8E into the first equation and solve for E. 8E+E = 180 9E = 180 E = 20 Degrees. This is the measure of an exterior angle. The interior angle is: I = 8E I = 8(20) I = 160 degrees. Now the measure of an interior angle of a regular polygon of n sides is given by: {{{I = (n-2)180/n}}} But we just found the measure of an interior angle: I = 160, so we substitute and solve for n. {{{160 = (n-2)(180)/n}}} Multiply both sides by n. {{{160n = 180n-360}}} Subtract 160n from both sides. {{{0 = 20n-360}}} Add 360 to both sides. {{{360 = 20n}}} Finally, divide both sides by 20. {{{n = 18}}} The regular polygon has 18 sides.