SOLUTION: in an octagon four of the angles are equal and each of others is 20 degree greater than each of first four.find the angles

Algebra ->  Polygons -> SOLUTION: in an octagon four of the angles are equal and each of others is 20 degree greater than each of first four.find the angles      Log On


   

Question 943927: in an octagon four of the angles are equal and each of others is 20 degree greater than each of first four.find the angles
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the interior angles of a polygon are (n-2)(180) where n is the number of sides. For an octagon, (8-2)(180)=6(180)=1080 degrees
let A =the smaller angles, A+20 the larger angles, the sum of four larger and four smaller=1080:
(4A)+(4(A+20))=1080 degrees
4A+4A+80=1080 degrees Subtract 80 from each side
8A=1000 degrees divide each side by 8
A=125 degrees ANSWER The smaller angles=125 degrees
A+20=125+20=145 ANSWER the larger angles =145 degrees
CHECK
Sum of interior angles of octagon=1080
4(125)+4(145)=1080 degrees
500 degrees+580 degrees=1080 degrees
1080 degrees=1080 degrees