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Two lines $p$ and $q$ intersect at $X$.  The angle between lines $p$ and $q$ is $45^\circ$.  Let $A$ be a point inside the $45^\circ$ angle formed by $p$ and $q$.  Let $B$ be the reflection of $A$ through line $p,$ and let $C$ be the reflection of $A$ through line $q.$  Find $\angle BXC,$ in degrees.

 
 May 6, 2024

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