Answer:
A
Explanation:
the diagonal from lower left to upper right is a true diagonal in the sense it cuts the octagon in half. it is like the diameter of a circle the octagon is inscribed in.
every corner of the octagon represents a 1/8 maker of the full 360° circle.
or 1/4 markers (5 vertexes with 4 sections between them) of 90° between the outermost right diagonal to the outermost left diagonal from one single vertex.
so, the drawn second diagonal is one marker left of the outermost right diagonal (which would be at a right angle to the first, true diagonal).
that means x is 1 - 1/4 = 3/4 of the 90° starting angle.
90×3/4 = 270/4 = 67.5°
FYI : the angle with the diagonal to the next vertex to the left would be 2/4 of 90° = 45°.
the angle with the diagonal to the vertex after that to the left (the left endpoint of the first, true diagonal) would be 1/4 of 90° = 22.5°
the angle with the diagonal to the the vertex after that to the left (which is now parallel to the first, true diagonal) would be 0°.