Answer: 22.5 degrees
Start by drawing a hexagon.
Connect segments CBD. We then form an isosceles triangle CBD.
We know triangle CBD is isosceles because a regular octagon has equal sides and angles. With that said, BC = CD, which are both legs in triangle CBD.
Then, we can use the angles formula to solve for angle BCD which is just a regular angle in the octagon.
The formula for an angle in a n-sided polygon is
where n is the number of sides.
Plugging "8" into the formula gives us 135 for each angle of the octagon.
Now we know that angle BCD = 135 degrees. We can use the fact that triangle CBD is isosceles so Angle CBD and angle CDB are equal. Let's call angle CBD = x.
We can write:
2x + 135 = 180 as the sum of the angles of a triangle is 180 degrees
Subtracting 135 from both sides gives us:
2x = 45
Dividing by 2 on both sides gives us:
x or angle CBD = 22.5
Hope this helps.