select all true statements if n || m.\na. m∠2 = 60\nb. m∠3 = 100\nc. m∠2 + m∠4 = 80\nd. m∠2 + m∠3 = 80\ne…

select all true statements if n || m.\na. m∠2 = 60\nb. m∠3 = 100\nc. m∠2 + m∠4 = 80\nd. m∠2 + m∠3 = 80\ne. m∠2 = 20

select all true statements if n || m.\na. m∠2 = 60\nb. m∠3 = 100\nc. m∠2 + m∠4 = 80\nd. m∠2 + m∠3 = 80\ne. m∠2 = 20

Answer

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}\neq80^{\circ}), so D is incorrect.

Answer:

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