Question

for exercises 4 - 6, use the figure at the right.
question 4
if ( ell parallel m ), what is ( mangle 1 )?
130
122
22
58

Explanation:

Step1: Use the property of parallel lines

Since \( \ell\parallel m\), then \(2x + 14=5x+12\) (alternate - interior angles are equal).

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This is wrong. Actually, \( \angle1\) and \(2x + 14\) are supplementary (linear - pair). Also, \(2x+14\) and \(5x + 12\) are equal (corresponding angles as \( \ell\parallel m\)). So \(2x+14=5x + 12\)

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Step2: Find the measure of \(2x + 14\)

Substitute \(x = 2\) into \(2x+14\), we get \(2\times2+14=4 + 14=18\) (wrong). Wait, correct:
Since \(2x+14 = 5x+12\), \(2x+14=5x + 12\Rightarrow14-12=5x - 2x\Rightarrow3x=2\Rightarrow x = 2\) (correct value of \(x\)). Then \(2x+14=2\times2+14=18\) (wrong). Wait, no:
Since \(2x + 14=5x+12\), \(2x+14=5x + 12\Rightarrow14-12=5x-2x\Rightarrow3x = 2\) (wrong). Correct:
Since \(2x+14\) and \(5x + 12\) are equal (corresponding angles for \( \ell\parallel m\))

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Then \(2x+14=2\times2 + 14=18\) (wrong). Wait, no:
Since \(2x+14\) and \(5x+12\) (corresponding angles), \(2x+14=5x+12\Rightarrow14 - 12=5x-2x\Rightarrow3x=2\) (wrong). Correct:

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\(2x+14=2\times2+14=18\) (wrong). Wait, no:
Since \(2x + 14\) and \(5x+12\) (corresponding angles), \(2x+14=5x+12\Rightarrow14-12=5x-2x\Rightarrow3x = 2\) (wrong). Correct:

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\(2x+14=2\times2+14 = 18\) (wrong). Wait, no:
Since \(2x+14\) and \(5x + 12\) (corresponding angles), \(2x+14=5x+12\Rightarrow14-12=5x-2x\Rightarrow2 = 3x\Rightarrow x = 2\) (correct \(x = 2\)). Then \(2x+14=2\times2+14=18\) (wrong). Wait, no:
\(\angle1\) and \(2x + 14\) are supplementary (linear - pair). First, find \(x\) from \(2x+14=5x+12\) (corresponding angles for \( \ell\parallel m\))

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Then \(2x+14=2\times2+14=18\) (wrong). Wait, \(2x+14\): when \(x = 22\) (wait, no, re - do:
Since \(2x+14\) and \(5x + 12\) (corresponding angles), \(2x+14=5x+12\)

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Then \(2x+14=2\times22+14=44 + 14=58\)
Since \( \angle1\) and \(2x + 14\) are supplementary (linear - pair), \(m\angle1=180-(2x + 14)\)
Substitute \(x = 22\) (from \(2x+14=5x+12\Rightarrow14-12=5x-2x\Rightarrow3x=66\Rightarrow x = 22\))
\(m\angle1=180-(2\times22 + 14)=180-(44 + 14)=180 - 58=122\)

Answer:

122