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Point $H$ is the orthocenter of $\triangle ABC$. If $\angle BAC=115^\circ$, what is $\angle BHC$ in degrees?

https://latex.artofproblemsolving.com/a/8/2/a82492d5292a38bbba7c8d64453264254ae9ef9f.png

 Nov 5, 2019
 #1
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Angle BHC is 55 degrees.

 Nov 5, 2019
 #2
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If BAC  =  115°.....then  angle EAF   also  = 115°   [vertical angles ]

 

So....in quadrilateral  EAFH  angle  FHE  =  angle BHC  =

 

360  -  angle EAF  = angle AFH - angle AEH   =

 

360  - 115 -  90  - 90   =

 

180  -  115   =

 

65°

 

cool cool cool

 Nov 5, 2019

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