We want to find the measure of the given angle such that makes lines u and v parallel.
The measure of the indicated angle must be 108° to make lines u and v parallel.
To find the angle we need to use two things.
1) If two lines n and m are parallel, then if a single line intersects these two, all the angles generated in line m must be exactly the same as the ones generated on line n.
2) In an intersection of two lines, two angles that are next to each other must add up to 180°.
By the first criteria, the missing angle that is represented with a "?" must have the exact same measure as the angle that is just below the 72° angle.
By the second criteria, (and the first one that we already used) we must have:
? + 72° = 180°
Solving that we get:
? = 180° - 72° = 108°
The measure of the indicated angle must be 108° to make lines u and v parallel.
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