x is the midpoint of $ \overline{uv} $, y is the midpoint of $ \overline{uw} $, and t is the midpoint of $ \overline{vw} $. if $ m \angle u = 56 ^ { \circ } $ and $ m \angle w = 49 ^ { \circ } $, find $ m \angle tyw $.
$ m \angle tyw = \square ^ { \circ } $ (simplify your answer.)

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# Explanation:
## Step1: Find $m\angle V$ in $\triangle UVW$
In $\triangle UVW$, by the angle - sum property of a triangle ($m\angle U+m\angle V + m\angle W=180^{\circ}$).
Substitute $m\angle U = 56^{\circ}$ and $m\angle W = 49^{\circ}$ into the formula:
$m\angle V=180-(56 + 49)=180 - 105=75^{\circ}$

## Step2: Use the mid - segment theorem
Since $X$ is the mid - point of $\overline{UV}$, $Y$ is the mid - point of $\overline{UW}$, and $T$ is the mid - point of $\overline{VW}$, $XY\parallel VW$ and $YT\parallel UV$ (mid - segment theorem: the segment connecting the mid - points of two sides of a triangle is parallel to the third side).
Quadrilateral $XYTV$ is a parallelogram (a quadrilateral with both pairs of opposite sides parallel). So $XY = VT$ and $YT=XV$. Also, $\angle TYW$ and $\angle V$ are corresponding angles (because $YT\parallel UV$ and $VW$ is a transversal).

# Answer:
$75$

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Explanation:

Step1: Find \(m\angle V\) in \(\triangle UVW\)

Step2: Use the mid - segment theorem

Answer: