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 alternate - interior angles

Since \(n\parallel m\), \(\angle2\) and the \(20^{\circ}\) angle are alternate - interior angles. So \(m\angle2 = 20^{\circ}\), E is correct, A is incorrect.

Step2: Use linear - pair and angle - sum properties

The angle adjacent to the \(60^{\circ}\) angle is \(120^{\circ}\). In the triangle formed by points \(A\), \(B\), and \(C\), we know one angle is \(20^{\circ}\) and another is \(120^{\circ}\).
The sum of angles in a triangle is \(180^{\circ}\). Let's find \(\angle3\).
We know that \(m\angle3=180-(20 + 60)=100^{\circ}\), so B is correct.

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

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

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

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

Answer:

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