In a town, the bearing of the library from the station is 𝑥∘. The theatre is due east of the library. The theatre and the station are equidistant from the library. What is the bearing (in degrees) of the station from the theatre?

Answer:

There are several approaches to solving this problem. One approach is given below.
Extend north line down at L and recall that alternate angles
between parallel lines are equal,
so angle SLT = 90 + 𝑥
Because the interior angles of any triangle add up to 180°,
LTS + LST = 180 − (90 + 𝑥)
LTS + LST = 90 − 𝑥.
Triangle SLT is isosceles so both angles LTS and LST = 90−𝑥
2
Bearing S from T = 270 − � 90−𝑥
2 � = 270 − 45 + 𝑥
2 = 225 + 𝑥
2
The answer is F