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 :

179°

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°