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Answers and explanations for various angle relationships and proofs related to parallel lines and a transversal. Topics include corresponding angles, supplementary angles, congruent angles, complementary angles, and finding unknown angle measures using theorems and given information.
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Find the value of the variable(s) in each figure. Explain your reasoning.
ANSWER: y = 114 by the Corresponding Angles Postulate; x = 54 by the Supplement Theorem
ANSWER: x = 63 by the Vertical Angle Theorem and the Consecutive Interior Angles Theorem
ANSWER: x = 54 by the Alternate Interior Angles Theorem; y = 12 by the Consecutive Interior Angles Theorem
STORAGE When industrial shelving needs to be accessible from either side, additional support is provided on the side by transverse members. Determine the relationship between each pair of angles and explain your reasoning.