Given:
5 angles are equal: x
Each of the other angles is 24 greater than the other 5 angles: x+24
An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º

Use the equation above to solve x:

The 5 angles that are equal measure 126º
The other 3 angles measure:

Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150º