Question

x is the midpoint of $overline{uv}$, y is the midpoint of $overline{uw}$, and t is the midpoint of $overline{vw}$. if $mangle w=41^{circ}$ and $mangle u=64^{circ}$, find $mangle uyx$.
$mangle uyx=\square^{circ}$ (simplify your answer.)

Explanation:

Step1: Find ∠UVW in △UVW

The sum of angles in a triangle is $180^\circ$.
$$m\angle UVW = 180^\circ - m\angle U - m\angle W = 180^\circ - 64^\circ - 41^\circ = 75^\circ$$

Step2: Prove XY || VW

X, Y are midpoints of $\overline{UV}$, $\overline{UW}$. By Midsegment Theorem, $XY \parallel VW$.

Step3: Find m∠UYX

Corresponding angles of parallel lines are equal. $\angle UYX$ and $\angle UVW$ are corresponding angles.
$$m\angle UYX = m\angle UVW = 75^\circ$$

Answer:

$75$