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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.

 Dec 28, 2023
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avatar+129742 
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Angle BDX = 90 = angle ADX

DA = BD

XD = XD

So, by LL, triangles BXD and AXD are congruent right triangles

And by the same reasoning triangles, AXE and CXE  are congruent right triangles

And angle DXE  = the angle formed by the intersection of  lines p,q = 45 = the sum of  angles AXD and   AXE

But angles  BXD and CXE  = angles AXD and AXE....so their sum is  also = 45

 

So angle BXC = AXD + AXE + BXD + CXE    =    45 + 45  =  90

 

cool cool cool

 Dec 28, 2023
edited by CPhill  Dec 28, 2023

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