If L is the circumcentre of ΔXYZ and angle X is 40°, then the value of ∠YZL is :
Answer & explanation
Correct answer: option 4
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°