(The angle bisectors) Math Help Quick Please!

m∠WPY = 92°

m∠WQZ = 18°

WZ = 22

Step-by-step 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

m∠WPY = 92°

m∠WQZ = 18°

WZ = 22