Question

HELP!
Line n ‖ line BC.
Which statements about the figure must be true?

Choose all answers that are correct.
A.
m∠1 = 45°

B.
m∠2 + m∠3 = 84°

C.
m∠2= 45°

D.
m∠3 = 45°

Answer 1

B) 
Because if you find the degrees for angle 1 you get:
180⁰ - 45⁰- 39⁰ = 96⁰ <- angle 1
The triangle in the center has 3 angles, and those 3 angles will equal 180⁰
So, 180⁰ - 96⁰ = 84⁰

Refer to the other answer to see how letter c was done

Answer 2

$m\angle 1=180-45-39=96 \Rightarrow \text{A not true}\\ m\angle 2+m \angle 3=180-m\angle 1=180-96=84 \Rightarrow \text{B true}$

$m \angle 2$ and the above angle with $45^{\circ}$ are alternate interior angles so $m \angle2 =45 \Rightarrow \text{C true}$

$m \angle3=180- m\anlge1 - m\angle 2\\ m \angle 3=180-96-45=39 \Rightarrow \text{ D not true}$