The angle marked x and the one marked 100° form a linear pair, so are supplementary. The measure of x is ...
x = 180° -100° = 80°
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The angle marked 40° and the one marked y are "alternate interior angles" with respect to the parallel lines and the diagonal that crosses them. As such, they have the same measure:
y = 40°
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The angle marked 100° and the sum of angles in the lower right corner are "corresponding" angles, so have the same measure. That is ...
