Angular reflection
Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
Age
11 to 14
Challenge level
Problem
Image
In the diagram, $\angle MON = 130^{\circ}$. The reflection of $OP$ in $OM$ is $OQ$ and the reflection of $OP$ in $ON$ is $OR$.
What is the size of $\angle QOR$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Image
As $OQ$ is the reflection of $OP$ in $OM$, $\angle QOM = \angle POM$.
Similarly, $\angle RON = \angle PON$.
Hence reflex $\angle QOR = 2 \times \angle MON = 260^{\circ}$
Therefore $\angle QOR =360^{\circ} - 260^{\circ} = 100^{\circ}$.