+1556 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?
+410 
\(\because \triangle TSU \sim \triangle TPM\)
\(\therefore \angle TMP = \angle TUS = {89}^{\circ}\)
\(\because \angle STU = {29}^{\circ}, \angle TZU = {90}^{\circ}\)
\(\therefore \angle TUZ = 180-29-90={61}^{\circ}\)
\(\therefore \angle TMZ + \angle TUZ = {160}^{\circ}\).
.
