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avatar+1347 

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively.  Let $\overline{UZ}$ be an altitude of the triangle.  If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, then what is $\angle ZNM + \angle ZMN + \angle PNM + \angle PMN + \angle NZM + \angle NPM$ in degrees?

 Jan 12, 2024
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avatar+128732 
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 We have triangle  MNZ

 

Angle ZNM  + Angle ZMN + Angle NZM  =  180°

 

And we have triangle  PNM

 

Angle PNM + Angle PMN  + NPM  =   180°

 

So....the sum  of all the given angles =  360°

 

 

cool cool cool

 Jan 12, 2024

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