Answer:
Explanation:
You want the values of x and z in the figure where one pair of parallel lines crosses another.
Transversal angles
Where a transversal crosses parallel lines, corresponding angles are congruent. This gives rise to several other relationships, each with its own name. The net result is that all acute angles are congruent, and all obtuse angles are congruent. The acute and obtuse angles are supplementary. (If the crossing is at right angles, then all angles are congruent.)
Application
Here, the angle marked x° is supplementary to the one marked 77°:
x = 180 -77 = 103
The angle marked (3z -19)° is congruent to the one marked 77°:
3z -19 = 77
3z = 96 . . . . . . add 19
z = 32 . . . . . . . divide by 3
The value of x is 103; the value of z is 32.
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Additional comment
The various pairs of angles at a transversal can be described as "consecutive", "alternate", "interior", "exterior", "same-side". Of course, where lines cross, the angles can also be "vertical" or "opposite" or "adjacent" or a "linear pair."
Depending on the relationship, the angles will be congruent or supplementary. For example, "alternate exterior angles" are congruent; "consecutive interior angles" are supplementary.
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