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

#1**+1 **

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...!!!

CPhill
Jul 28, 2017