Two railway tracks and are laid straight across a level crossing
MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles
Problem
Two railway tracks t1 and t2 are laid straight across a level crossing. A straight road intersects both tracks, meeting t1 at point M and t2 at point N. The angle between the road and track t1 on the north–east side of the crossing is 42∘. Solve the following parts:
(i) Assuming the tracks are parallel, find the measure of the angle between the road and track t2 on the north–east side.
(ii) Determine the acute angle between the road and track t2 on the south–west side.
(iii) If the angle between the road and track t2 on the south–west side is found by surveyors to differ from your answer in part (ii) by 3∘, discuss what this implies about the parallelism of the tracks, giving reasons.