Answer:
[tex]135^{\circ}[/tex]
Step-by-step explanation:
The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, the sum of its interior angles is equal to:
[tex](8-2)180=6\cdot 180=1,080^{\circ}[/tex]
By definition, a regular polygon is a polygon with equal sides and angles. An octagon has 8 sides and 8 angles. Therefore, a each interior angle of a regular octagon must be equal to:
[tex]\frac{1,080}{8}=\boxed{135^{\circ}}[/tex]
