Answer:
x = 135 degrees
Explanation:
The measure of each interior angle of a regular polygon is given by = (n-2)×180/n where n is the number of sides.
So for the regular octagon the measure of each interior angle is (8-2)×180/8 = 135
y = 135-90
y = 45 degrees
———
y + y + z = 135
90 + z = 135
z = 45 degrees
———
v = w = 90 (alternate interior angles of parallel lines)
———
z + w + w + x = 360 (angles in a quadrilateral add to 360)
45 + 90 + 90 + x = 360
225 + x = 360
x = 135 degrees
Good Luck!