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jmc

prealgebra intermediate

Problem

Lines , , and are coplanar, and they are drawn such that is parallel to , and is perpendicular to . If the measure of angle 1 is 50 degrees, what is the measure in degrees of angle 2 in the figure below?

problem
Solution
The intersection of these lines creates a triangle shown in the figure. Starting from the vertex closest to angle 2 and moving clockwise, label the triangle's vertices , , and . Since is a vertical angle of angle 1, it is equal to 50 degrees. Since is a right angle (the two lines intersecting to form the angle are perpendicular) and since the interior angles in the triangle sum to 180 degrees, degrees. Since angle 2 is supplementary to , angle 2 is equal to degrees.
Final answer
140