Geometry

Question Analysis

This question involves solving for the variables x and y given two parallel lines cut by a transversal, with angle measures expressed algebraically. The focus is on identifying the relationship between given angles and using it to set up an equation for x and y.

Key Concept Explanation:

When two parallel lines are cut by a transversal, corresponding angles are in the same relative position at each intersection. The key property is that corresponding angles are congruent.

A linear pair of angles is formed when two lines intersect. The two angles in a linear pair are adjacent, share a common side, and their non-common sides form a straight line. Their sum is 180 degrees.

Step-by-Step Solution:

Solve for x:

In this problem, the angles (3x + 72)° and (11x - 116)° are linear pair angles, so we can set their measures to be supplementary (add up to 180) and solve for x:

(3x + 72) + (11x - 116) = 180

14x - 44 = 180

14x = 224

x = 16

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