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Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

 Jun 20, 2024

Best Answer 

 #1
avatar+1252 
+1

Before we solve the problem, let's note something important. 

The sum of the angles in a triangle must add up to \(180 ^\circ\)

 

However, let's take a look at something. 

Adding up the two angles we have, we get \(144 + 66 = 210°\)

This means that triangle AHB would have angles adding up to more than 180. 

 

Thus, this is an invalid triangle. 

 

Thanks! :)

 

~NTS

 Jun 21, 2024
edited by NotThatSmart  Jun 21, 2024
 #1
avatar+1252 
+1
Best Answer

Before we solve the problem, let's note something important. 

The sum of the angles in a triangle must add up to \(180 ^\circ\)

 

However, let's take a look at something. 

Adding up the two angles we have, we get \(144 + 66 = 210°\)

This means that triangle AHB would have angles adding up to more than 180. 

 

Thus, this is an invalid triangle. 

 

Thanks! :)

 

~NTS

NotThatSmart Jun 21, 2024
edited by NotThatSmart  Jun 21, 2024

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