### Instruction: Sides $\overline{AH}$ and $\overline{CD}$ of regular octagon $ABCDEFGH$ are extended to meet at point $P$. What is the degree measure of angle $P$?### Response: I know that the sum of the interior angles of a regular octagon is $180(8 - 2) = 1080$ degrees, and that each interior angle is $\frac{1080}{8} = 135$ degrees.
So, angle $A$ and angle $D$ are both $135$ degrees.
I also know that the exterior angle of a regular polygon is the supplement of the interior angle, so angle $H$ and angle $C$ are both $180 - 135 = 45$ degrees.
Now, I can use the fact that the sum of the angles in a triangle is $180$ degrees to find angle $P$.
Angle $P$ is part of triangle $PCH$, and I already know that angle $H$ and angle $C$ are both $45$ degrees.
So, angle $P = 180 - 45 - 45 = 90$ degrees.