Which of the following can't represent the degree measure of an equian

Solution:

Recall that the sum of the measures of all the angles of an n-sided polygon is 180(n - 2) degrees. Therefore, if the polygon is equiangular, the measure of each angle is m = 180(n - 2)/n degrees. Now let’s check each answer choice.

A) 160

If m = 160, we have:

160 = 180(n - 2)/n

160n = 180n - 360

360 = 20n

18 = n

So m can be 160.

B) 150

If m = 150, we have:

150 = 180(n - 2)/n

150n = 180n - 360

360 = 30n

12 = n

So m can be 150.

C) 140

If m = 140, we have:

140 = 180(n - 2)/n

140n = 180n - 360

360 = 40n

9 = n

So m can be 140.

D) 130

If m = 130, we have:

130 = 180(n - 2)/n

130n = 180n - 360

360 = 50n

7.2 = n

Since n must be an integer, we see that m CAN’T be 130.

Alternate Solution:

Recall that the sum of the measures of all the angles of an n-sided polygon is 180(n - 2) degrees. Therefore, if the polygon is equiangular, the measure of each angle is m = 180(n - 2)/n degrees. Let’s solve this equation for n:

nm = 180n - 360

360 = 180n - nm

360 = n(180 - m)

n = 360/(180 - m)

Since the number of sides in a polygon is an integer, n = 360/(180 - m) must be an integer. Checking each answer choice, we notice that all the choices except m = 130 result in an integer value for n.

Answer: D