Question

if ( n parallel m ), which of the following statements are true? select all that apply
a ( m angle 2 = 60 ^ { circ } )
b ( m angle 3 = 100 ^ { circ } )
c ( m angle 2 + m angle 4 = 80 ^ { circ } )
d ( m angle 2 + m angle 3 = 80 ^ { circ } )

Explanation:

Step1: Find \(m\angle1\)

Since \(n\parallel m\), \(\angle1\) and the \(60^{\circ}\) angle are alternate - interior angles. So \(m\angle1 = 60^{\circ}\).

Step2: Find \(m\angle2\)

\(\angle2\) and the \(20^{\circ}\) angle are alternate - interior angles. So \(m\angle2=60^{\circ}\) (because \(n\parallel m\), and using the property of alternate - interior angles).

Step3: Analyze \(\angle3\) and \(\angle4\)

Since \(n\parallel m\), \(\angle1\) and \(\angle4\) are alternate - interior angles (\(m\angle4 = 60^{\circ}\)), and \(\angle2\) and the \(20^{\circ}\) angle are alternate - interior angles.
For option A: \(m\angle2 = 60^{\circ}\) (calculated from alternate - interior angles property).
For option B: \(m\angle3=180^{\circ}-(m\angle2 + 60^{\circ})\). Since \(m\angle2 = 20^{\circ}\), \(m\angle3 = 100^{\circ}\) (using the angle - sum property of a triangle formed by the transversal and the parallel lines).
For option C: \(m\angle2+m\angle4=20^{\circ}+60^{\circ}=80^{\circ}\)
For option D: \(m\angle2 + m\angle3=20^{\circ}+100^{\circ}=120^{\circ}\)

Answer:

A. \(m\angle2 = 60^{\circ}\), B. \(m\angle3 = 100^{\circ}\), C. \(m\angle2 + m\angle4 = 80^{\circ}\)