In the given figure, chords AD and BC in the circle, are extended to E and F, respectively.
If ∠CDE = 85°, ∠DCF = 94°, then the value of ∠ABF + ∠EAB is :
Answer & explanation
Correct answer: option 2
We know that,
Sum of two angles forming a linear pair = 180°.
Sum of opposite angle of cyclic quadrilateral = 180°.
∠CDE = 85°
∠DCF = 94°
We know that,
∠CDE + ∠ADC = 180°
= 85° + ∠ADC = 180°
= ∠ADC = 95°
Now, ∠ABC + ∠ADC = 180°
= ∠ABC + 95° = 180°
= ∠ABC = 85°
= ∠ABF = 85° ----(a)
Similarly, ∠EAB = 94° ----(b)
From (a) and (b),
= ∠ABF + ∠EAB = 179°