is a line of symmetry going through the center of an octagon parallel to the ground it is on?

Question

I came across this question recently, It wanted me to find angle EDG assuming the line crossing between the octagon/polygon is it's line of symmetry.

My answer was 25 degrees, but A few friends said it was 70, I used alternate angles (the line of symmetry and the base) to find the angle of line ED to the base then subtract the exterior angle from the result.

This produces a valid looking answer using a valid theory (I suppose) but my friends claim is that Angles BAF, BCD, CDE and EFA = 65 degrees because the internal angles of the polygon must be 540 degrees and they believe BAF, BCD, CDE and EFA are equal. Am I right to assume that the line of symmetry provided must be parallel to the base?

Answer 1

Yes, the line of symmetry is parallel to the base.

Since you have a line of symmetry, the edges through the line of symmetry must be unchanged by the reflection: the line of symmetry needs to be perpendicular to the vertical edges, hence horizontal, just like the base.

I agree with your answer of $25^\circ$ for $\angle EDG $.

Answer 2

What is 65 degrees? Except that, your answer and all else you said above is correct.