Parallel Base
Age
11 to 14
Challenge level
Weekly Problem 46 - 2015
The diagram shows two parallel lines and two angles. What is the value of x?
Problem
In the diagram $ST$ is parallel to $UV$.
Image
What is the value of $x$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Since $ST$ is parallel to $UV$, $\angle PRT$ and the angle of size $132^{\circ}$ are corresponding angles, so $\angle PRT=132^{\circ}$.
Since angles on a straight line sum to $180^{\circ}$ we must have $\angle PRQ=48^{\circ}$.
From the exterior angle of a triangle theorem, $\angle SQP=\angle QPR + \angle PRQ$,
so $134=x+48$, that is, $x=86$.