A straight road intersects two railway tracks at points and that are apart
MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles
Problem
A straight road intersects two railway tracks at points M and N that are 200m apart. On the same side of the road, the angle between the road and the first track is (3w+25)∘, while the angle between the road and the second track is (7w−55)∘. Assume the tracks are straight and lie in the same plane.
(i) Find the value of w.
(ii) Show that the two railway tracks are parallel.
(iii) A new service road cuts the two tracks on the opposite side of the original road, making an interior angle of 60∘ with the first track. Calculate the interior angle it must make with the second track so that the tracks remain parallel.