Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $ riangle XYZ$ intersect at point $H$. If the altitudes intersect at a $123^\circ$ angle, and $\angle YXH = 26^\circ$, then what is $\angle HZX$ in degrees?

Question

Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $	riangle XYZ$ intersect at point $H$. If the altitudes intersect at a $123^\circ$ angle, and $\angle YXH = 26^\circ$, then what is $\angle HZX$ in degrees?

AoPS · Answer

Sally, if you don't stop this cheating, we will have to deactivate your AoPS account. Why don't you ask your peers for some help on our message boards? ~AoPS

Anonymous · Answer

the answer should be approx 37 degrees.

anonymous · Answer

Whats the exact answer??

Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes intersect at a $123^\circ$ angle, and $\angle YXH = 26^\circ$, then what is $\angle HZX$ in degrees?