Question

2.06: swbat determine whether lines are parallel or not based on given angles
complete the following problems by showing all of your work for full credit.
**#1.) in the diagram below ( m angle 2 = 37 ^ { circ } ) and ( m angle 6 = 37 ^ { circ } ).
explain whether ( overleftrightarrow { a b } ) is parallel to ( overleftrightarrow { c d } ).
*#2.) in the diagram below ( m angle 1 = ( 12 x - 16 ) ^ { circ }, m angle 4 =)( ( 2 x + 24 ) ^ { circ }, m angle 7 = ( 39 y - 8 ) ^ { circ } ), and ( m angle 8 = ( y + 28 ) ^ { circ } ). solve for
angles 1, 4, 7, and 8.
a. using the angles found above, is ( p ) is parallel to ( q ) ? yes or no
b. explain your answer using the appropriate angle relationship.

Explanation:

Step1: Recall the corresponding angles postulate

If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. In the first problem, \(\angle2\) and \(\angle6\) are corresponding angles. Given \(m\angle2 = 37^{\circ}\) and \(m\angle6=37^{\circ}\), so \(\angle2\cong\angle6\).

Step2: Apply the postulate to determine parallelism for problem 1

By the corresponding angles postulate, since \(\angle2\) and \(\angle6\) (corresponding angles) are congruent, \(\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}\).

Step3: Solve for \(x\) in problem 2

\(\angle1\) and \(\angle4\) are vertical angles. Vertical angles are congruent. So \(m\angle1 = m\angle4\).

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Then \(m\angle1=12x-16=12\times4-16 = 32^{\circ}\), \(m\angle4=2x + 24=2\times4+24=32^{\circ}\)

Step4: Solve for \(y\) in problem 2

\(\angle7\) and \(\angle8\) are supplementary (linear - pair of angles). So \(m\angle7+m\angle8 = 180^{\circ}\)

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Then \(m\angle7=39y-8=39\times4-8 = 148^{\circ}\), \(m\angle8=y + 28=4+28 = 32^{\circ}\)

Step5: Check parallelism for problem 2 part a and b

\(\angle4\) and \(\angle8\) are corresponding angles. \(m\angle4 = 32^{\circ}\) and \(m\angle8=32^{\circ}\).
By the corresponding angles postulate, since \(\angle4\cong\angle8\) (corresponding angles), \(p\parallel q\)

Answer:

1. \(\overleftrightarrow{AB}\) is parallel to \(\overleftrightarrow{CD}\) because \(\angle2\) and \(\angle6\) (corresponding angles) are congruent (\(m\angle2=m\angle6 = 37^{\circ}\))
2. \(m\angle1 = 32^{\circ}\), \(m\angle4=32^{\circ}\), \(m\angle7 = 148^{\circ}\), \(m\angle8=32^{\circ}\)

• a. Yes
• b. \(p\parallel q\) because \(\angle4\) and \(\angle8\) (corresponding angles) are congruent (\(m\angle4=m\angle8 = 32^{\circ}\))