Answer:
m∠WPY = 92°
m∠WQZ = 18°
WZ = 22
Explanation:
PZ is the angle bisector of m∠QPR
and m∠QPR = m∠WPY
So m∠WPZ = half of m∠QPR = half of m∠WPY
If m∠WPZ = 46° ⇒ m∠WPY = 46 x 2 = 92°
If m∠XRY = 52° and m∠WPY = 92° then
m∠WQX = 180 - 52 - 92 = 36°
If QZ is the angle bisector of m∠PQR and m∠PQR = m∠WQX
then m∠WQZ = half of m∠WQX = 1/2 of 36 = 18°
ΔWQZ ≅ ΔQXZ
so WZ = XZ = 22