Question

select all true statements if n || m. a m∠2 = 60 b m∠3 = 100 c m∠2 + m∠4 = 80 d m∠2 + m∠3 = 80 e m∠2 = 20

Explanation:

Step1: Use corresponding - angles property

Since \(n\parallel m\), the angle corresponding to the \(60^{\circ}\) angle and \(\angle2\) are equal. So \(m\angle2 = 60^{\circ}\).

Step2: Use linear - pair property

The angle adjacent to the \(60^{\circ}\) angle and \(\angle1\) form a linear - pair. So \(m\angle1=120^{\circ}\). In the triangle formed by points \(A\), \(B\), and \(C\), we know one angle is \(20^{\circ}\) and another (\(\angle1\)) is \(120^{\circ}\). Using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle), we find \(m\angle3=180-(20 + 120)=40^{\circ}\).

Step3: Analyze angle relationships

\(\angle2\) and \(\angle4\) are vertical angles, so \(m\angle4 = m\angle2=60^{\circ}\), then \(m\angle2 + m\angle4=120^{\circ}\). Also, \(m\angle2+m\angle3=60 + 40=100^{\circ}\).

Answer:

A. \(m\angle2 = 60\) (True)
B. \(m\angle3 = 100\) (False)
C. \(m\angle2 + m\angle4 = 80\) (False)
D. \(m\angle2 + m\angle3 = 80\) (False)
E. \(m\angle2 = 20\) (False)
So the only true statement is A.