If L is the circumcentre of  ΔXYZ and angle X is 40°, then the value of ∠YZL is :

50°

We have,

∠X = 40° 

then we know that,

∠L  = 2∠X (By circumcentre property) 

= ∠YLZ  = 2∠YXZ

= ∠YLZ = 2 × 40°

= ∠YLZ = 80°

Now, In  ΔLYZ

LY = LZ (radius of the circle)

then, = ∠LYZ = ∠LZY 

 ∠ZYL + ∠YZL + ∠YLZ = 180° 

= 2∠YZL = 180° -  80° = 100°  

= ∠YZL = 50°