Answer:
If M and N are parallel, then the correspondent angles generated by the intersection with line R (or line S) should be equal.
So, if M and N are parallel, we should get that angles 2 and angle 4 are equal, as both of these are on the fourth quadrant of the intersection with the same line.
Similarly, if R and S are parallel, then correspondent angles generated by the intersection with line M (or line N) should be equal, this means that:
angle 3 and angle 7 should be equal.
Also remember that if we have two lines intersecting, generating 4 angles, any pair of two adjacent angles will always add to 180°.
Here we have two cases:
1) m∠3=69°, m∠7=71°
Here we can see that:
m∠3 ≠ m∠7
Thus, lines R and S are not parallel.
And here we do not have any information on the angles 1, 2, 5, and 6, so we can't compare the angles generated by line N with the ones generated by line M, so we can not know if lines N and M are parallel or not.
2) Now we have that:
m∠3=76° , m∠8=114°
Notice that angle 8 and angle 7 are adjacent, then we have that:
∠7 + ∠8 = 180°
And we know that:
∠8 = 114°
Then:
∠7 + 114° = 180°
∠7 = 180° - 114° = 76°
Then we have:
∠7 = ∠3
From this we can conclude that lines R and S are parallel.
(again, we can not do anything with lines N and M)
