This problem is actually not that difficult to solve, but it does
require several steps to determine the measures of both angles
since there is no direct relationship between the two. First,
angles 13 and 10 are vertical angles and therefore congruent.
So the measure of each angle is 1/2 of their sum, or 80°. Next,
angles 10 and 11 are same side interior angles (along transversal d and both on the inside of parallel lines a and b) and
therefore supplementary, so the measure of ∠11 must be
180° − 80° = 100°.
Now find the measure of ∠4. ∠11 and ∠7 are same side interior
angles (along transversal b and both on the inside of parallel
lines c and d) and so are supplementary. Therefore the measure
of ∠7 = 180° − 100° = 80°; ∠7 and ∠4 are vertical angles, and so
the measure of ∠4 must also be 80.
The measure of ∠11 is greater than the measure of ∠4 because
100° > 80°. The answer is b.
With some practice, you will become familiar with the
relationships between the angles created by a transversal cutting
two parallel lines. This will make analyzing a system of multiple
parallel lines and transversals much easier, and you will be able
to quickly intuit the relationship between angles like these by
logically connecting different pairs of congruent and
supplementary angles. Once you know the basic rules it
becomes easier and easier to break down the components of a
complicated system of lines and angles to solve the problem.