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 \(20^{\circ}\) angle is \(\angle2\). So \(m\angle2 = 20^{\circ}\), which means option E is correct and option A is incorrect.

Step2: Use linear - pair and parallel - lines properties

The angle adjacent to the \(60^{\circ}\) angle on line \(n\) is \(180 - 60=120^{\circ}\). Consider the triangle formed by points \(A\), \(B\), and \(C\). The sum of angles in a triangle is \(180^{\circ}\).
We know one angle of the triangle is \(20^{\circ}\) (the angle at \(A\)) and the other non - \(\angle3\) angle is \(60^{\circ}\) (the angle at \(C\)).
So \(m\angle3=180-(20 + 60)=100^{\circ}\), option B is correct.

Step3: Analyze \(\angle2+\angle4\)

\(\angle4\) and the \(60^{\circ}\) angle are vertical angles, so \(m\angle4 = 60^{\circ}\). Then \(m\angle2+m\angle4=20 + 60=80^{\circ}\), option C is correct.

Step4: Analyze \(\angle2+\angle3\)

\(m\angle2 + m\angle3=20+100 = 120^{\circ}
eq80^{\circ}\), option D is incorrect.

Answer:

B. \(m\angle3 = 100\)
C. \(m\angle2 + m\angle4 = 80\)
E. \(m\angle2 = 20\)