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Altitudes XD and YE of acute triangle XYZ intersect at point H. If the altitudes intersect at a 123 degree angle, and angle YXH=26 degrees, then what is angle HZX in degrees?

bbelt711  Jul 28, 2017
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Draw altitude ZF through orthocenter H

 

Angle XHE is supplemental to angle YHD  = 180° - 123°  = 57°

And since XEH = 90°....then angle HXE  = angle XEH - angle XHE = 90° - 57° =  33°

And YXH  = 26° , then YXZ   = YXH + HXE =  26° + 33°  =   59°

 

So...triangle FZX is right with FXZ  = 59°, angle ZFX  = 90° and angle FZX  = angle HZX   = 180° - FXZ - ZFX  = 180° - 59° - 90°  = 31°

 

Thanks to hectictar for catching my previous error...!!!

 

 

 

cool cool cool

CPhill  Jul 28, 2017
edited by CPhill  Aug 3, 2017

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