Answer:
m∠WXY=127°
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle XYW
we know that
The diagonal of symmetry divides the kite into two congruent triangles and it also bisects the pair of opposite angles.
The diagonal of symmetry is the segment WY (see the attached figure)
so
m∠XYW=m∠ZYW
we have
m∠ZYW=15°
so
m∠XYW=15°
step 2
Find the measure of angle WXY
Remember that
The sum of the interior angles in a triangle must be equal to 180 degrees
so
In the triangle XYW
m∠XYW+m∠XWY+m∠WXY=180°
we have
m∠XYW=15°
m∠XWY=38°
substitute the values
15°+38°+m∠WXY=180°
53°+m∠WXY=180°
m∠WXY=180°-53°
m∠WXY=127°
