Finding $\angle QCA$ from Altitude $AM$ of Triangle $ABC$

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SUMMARY

The discussion focuses on calculating the angle $\angle QCA$ in triangle $ABC$ given specific angle measures. The angles provided are $\angle QBA = 20^{\circ}$, $\angle QBC = 40^{\circ}$, and $\angle QCB = 30^{\circ}$. Using the properties of triangles and the sum of angles, the conclusion is drawn that $\angle QCA$ can be determined through geometric relationships inherent in triangle $ABC$. The solution emphasizes the importance of understanding triangle angle properties for accurate calculations.

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If $Q$ is a point on the altitude $AM$ of triangle $ABC$, and that $\angle QBA=20^{\circ}$, $\angle QBC=40^{\circ}$ and $\angle QCB=30^{\circ}$, find $\angle QCA$.
 
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anemone said:
If $Q$ is a point on the altitude $AM$ of triangle $ABC$, and that $\angle QBA=20^{\circ}$, $\angle QBC=40^{\circ}$ and $\angle QCB=30^{\circ}$, find $\angle QCA$.
Point Q must be the orthocenter of
$\triangle ABC $
we have :$\angle QCA+30+40=90$
$\therefore \angle QCA=20^o$
 
Albert said:
Point Q must be the orthocenter of
$\triangle ABC $
we have :$\angle QCA+30+40=90$
$\therefore \angle QCA=20^o$

Well done, Albert! Well done!(Yes) And thanks for participating!
 

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