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?

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1. using the fact that the acute angles of right triangles are complementary, and that vertical angles are equal, it's pretty easy to determine that HXZ is 31°

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posted by Steve
2. Stop cheating on AoPS challenge problems!

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posted by AoPS
3. 31 it is!

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posted by InfaRed
4. how is he

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posted by @AoPS

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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?

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