A, B, C, D and E lie on the circle. AB is extended to F. Angle AED = 140 ° and angle CBF = 95°. Find the values of w , x and y
Answers
Given : A Figure having circle , A , B , C , D & E lie son circle , AB is extended to F ∠AED = 140° & ∠CBF = 95°
To Find : w ,x , & y
Solution:
ABDE is a cyclic quadrilateral
=> ∠ABD + ∠AED = 180° ( Sum of opposite angle of cyclic quadrilateral = 180°)
=> w° + 140° = 180°
=> w° = 40°
Now ∠ABD + ∠DBC + ∠CBF = 180° ( straight line)
∠ABD° = w = 40° , ∠CBF = 95°
=> 40° + ∠DBC + 95° = 180°
=> ∠DBC = 45°
∠DAC = ∠DBC ( angle by same chord CD)
=> ∠DAC = 45°
=> y° = 45°
∠ACD = ∠ABD ( angle by same chord AD)
=> ∠ACD = w = 40°
in ΔACD
x° + y° + 40° = 180°
=> x° + 45° + 40° = 180°
=> x° = 95°
x° = 95° , y° = 45° , w° = 40°
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