Question

4.12 unit test: angles - part 1
due: fri oct 17, 2025 11:59pm
attempt 1
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available: oct 8, 2025 12:00am until dec 18, 2025 11:59pm
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in the figure, ( a parallel e, m parallel n ), and ( m angle 4 = 97 ^ { circ } ).
what is the sum of ( m angle 2 ) and ( m angle 4 )?
enter your answer in the box.
( square ^ { circ } )

Explanation:

Step1: Find the measure of ∠2

Since \(a\parallel e\) and \(m\parallel n\), \(\angle2\) and \(\angle4\) are same - side interior angles.
For parallel lines \(a\parallel e\) and transversal \(m\) (or \(n\)), the sum of same - side interior angles is \(180^{\circ}\).
Let \(m\angle2=x\) and \(m\angle4 = 97^{\circ}\).
We know that \(x+97^{\circ}=180^{\circ}\) (same - side interior angles theorem).
So, \(x=m\angle2=180^{\circ}-97^{\circ}\)
\(m\angle2 = 83^{\circ}\)

Step2: Calculate the sum of \(m\angle2\) and \(m\angle4\)

We need to find \(m\angle2 + m\angle4\).
Substitute \(m\angle2 = 83^{\circ}\) and \(m\angle4=97^{\circ}\) into the sum.
\(m\angle2 + m\angle4=83^{\circ}+97^{\circ}\)

Answer:

\(180\)