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Geometry and Trigonometry
Difficulty: Medium
In the figure, line is parallel to line , and both lines are intersected by line . If , what is the value of ?
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Explanation
The correct answer is . Based on the figure, the angle with measure and the angle vertical to the angle with measure are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure also has measure . It’s given that lines and are parallel. Therefore, same side interior angles between lines and are supplementary. It follows that . If , then the value of can be found by substituting for in the equation , which yields , or . Subtracting from both sides of this equation yields . Dividing both sides of this equation by yields . Thus, if , the value of is .