Question

in an octagon five of the angles are equal and each of the other three angles is 24 greater than each of the five other ones determine the angles of the octagon

Answer 1

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