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?

Suvi · Accepted Answer

All you guys need to chill out. Sometimes people, LIKE ME, need help on courses while their parents are busy and want to figure out the solutions and try them themselves so they can still learn. IT AINT ANY OF UR BUISNESS

Steve · Answer

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°

AoPS · Answer

Stop cheating on AoPS challenge problems!

InfaRed · Answer

31 it is!

@AoPS · Answer

how is he

AoPS · Answer

Yep it's 31.

AoPS helper · Answer

Y'all ur wasting like 500 dollars on a course that you need for your life to get past the SAT. The SAT has a whole massive section in the math section that is completely based off of geometry.

Someone · Answer

Ya know, just reread the transcript, take notes, and if you have half a brain cell and some time, you should be able to figure it out am i wrong

idk · Answer

whats aops

Anonymous · Answer

AoPS is a math class. Art Of Problem Solving. Solving them BY YOURSELF! if you need help there is message board. and even if you do search the answer, at least understand why that answer is what it is!

CluckLord62 · Answer

True, so true

jjj · Answer

aops is good

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?