Step-by-step explanation:
Given: X is midpoint of UV and Y is midpoint of VW.
[tex] \therefore XY || UW[/tex]
(By mid-point theorem)
[tex]\therefore \angle XYV \cong \angle UWY\\.. (corresponding\: \angle 's) \\\therefore m\angle XYV = m\angle UWY\\
\therefore 98 - 6x = 63- x\\
\therefore 98 - 63= 6x- x\\
\therefore 35= 5x\\\\
\therefore x = \frac{35}{5}\\\\
\huge \orange {\boxed {\therefore x = 7}} \\\\
m\angle UWY = (63 - x) °\\\\
\therefore m\angle UWY = (63 - 7) °\\\\
\huge \purple {\boxed {\therefore m\angle UWY = 56 °}}
[/tex]
