all angles of a polygon are either 155 or 140 degrees. there are twice as many angles of 155 degrees as 140 degrees. find the number of sides of the polygon

Question

calculate the number of sides of the polygon

Answer 1

Let x=no. of 140 degree angles, then there are 2x 155 degree angles. Therefore the polygon has 3x sides and angles. The total of all the angles is 140x+155(2x)=140x+310x=450x degrees. The total angle sum of an n-gon is 90(2n-4)=180n-360 degrees. So n=3x, and the total angle sum=540x-360=450x, 90x=360, x=4, and n=12. So the polygon has 12 sides. 

CHECK

The interior angle of a regular 12-gon is 150°, making the angle sum=1800°. 4×140+8×155=560+1240=1800°. The angle sum of all 12-gons is the same as for a regular 12-gon.

Answer 2

i don't know