45 degrees, for the adjoining angles of the straight edges. Otherwise, the straight edges would be 180 degrees and 90 degrees.
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an octagon (8-sided)
It is a regular 8 sided octagon
Interior angle: 135 degrees Exterior angle: 45 degrees
If it is a regular 8 sided octagon then each interior angle is 135 degrees
For any REGULAR n-sided polygon the interior angles are (180 - 360/n) degrees eg for a regular octagon, where n = 8, the calculation is 180 - 360/8 ie 180 - 45 = 135o degrees.