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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
- PROOF Copy and complete the proof of Theorem 3.2. Given: is a transversal. Prove: 1 and 2 are supplementary; 3 and 4 are supplementary. Proof: ANSWER:
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.
- 1 and 5 ANSWER: Congruent; Corresponding angles
- 1 and 2 ANSWER: Complementary; because the vertical and horizontal lines are perpendicular, they form right angles.
- REASONING Determine the minimum number of angle measures you would have to know to find the measures of all the angles formed by two parallel lines cut by a transversal. Explain. ANSWER: One; sample answer: Once the measure of one angle is known, the rest of the angles are either congruent or supplementary to the given angle.
