1. It is fairly tedious to use construction techniques on paper to rotate a figure 90°, and somewhat error-prone to use a protractor. So, the attached makes use of a geometry program to rotate the parallel lines. In each case, XE is rotated to X'E.
d) You notice the resulting lines A'B' and C'D' are both perpendicular to the original AB and CD and are parallel to each other. They are the same distance apart that they were. (Rotation does not change distances or angles.)
2.
a) ∠ABC is supplementary to ∠CBD, so has measure 180°-50° = 130°.
b) ∠EBD is a vertical angle to ∠ABC, so has the same measure, 130°.
c) ∠ABE is a vertical angle to ∠DBC, so has the same measure, 50°.
