if L is the circumcentre of triangle XYZ and angle X is 40° then the value of angle YZL is
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Given : L is the circumcenter of triangle XYZ and angle X is 40
To Find : the value of angle YZL is
Solution:
L is the circumcenter of triangle XYZ
=> X , Y and ZZ lies on a circle whose center is L
=> LX = LY = LZ
∠X = 40° => ∠YXZ = 40°
=> ∠YLZ = 2∠YXZ = 2 x 40° = 80°
now in ΔYLZ
YL = YZ
=> ∠YZL = ∠ZYL
∠YZL + ∠ZYL + ∠YLZ = 180° ( sum of angles of triangle)
=> 2∠YZL + 80° = 180°
=> 2∠YZL = 100°
=> ∠YZL = 50°
value of angle YZL is 50°
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