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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 $\angle TSU = 62^\circ$ and $\angle STU = 29^\circ$, then what is $\angle TMP + \angle TUZ$ in degrees?

 Jan 28, 2025
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Since M is the midpoint of TU  and P  is the midpoint of ST, then MP divides sides TU and TS of triangle TUS proportionally...so  ....MP is parallel to US

So  angle TMP  = angle TUS  = 89

Angle TZU = 90   Angle UTS  = 29

So angle TUZ =  90 - 29  =  61

So angles TMP  + TUZ  =  89 + 61 =  150

 

cool cool cool

 Jan 28, 2025

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