Two parallel lines with a transversal form corresponding angles. Remember, lines are parallel if they never intersect. This is typically denoted by arrow symbols on the lines. A transversal is a line that crosses both of these parallel lines. The corresponding angles are in the same relative position about each parallel line and are congruent.
In this problem, you’re being asked to find angle x. Start with what you’re given.
Well we know that we have parallel lines because they have the same number of arrows on them. Again your textbook it might have an arrow filled in, but it means the exact same thing, these two lines are in the same plane and will never intersect.
We know that with two parallel lines and a transversal, corresponding angles will always be congruent. Well one pair of corresponding angles are these two obtuse angles. Another pair is 30 degrees and x. Since they are corresponding, they must be congruent, so x is 30 degrees, and you have your answer because you know corresponding angles are always congruent when you have two parallel lines cut by a transversal.