Question 69

In the given figure, chords AD and BC in the circle, are extended to E and F, respectively.

If $$\angle$$CDE = 85$$^\circ$$, $$\angle$$DCF = 94$$^\circ$$, then the value of $$\angle$$ABF + $$\angle$$EAB is:

Solution

From the figure,

$$\angle$$CDE + $$\angle$$CDA = 180$$^\circ$$

$$=$$>  85$$^\circ$$ + $$\angle$$CDA = 180$$^\circ$$

$$=$$>  $$\angle$$CDA = 95$$^\circ$$

$$\angle$$DCF + $$\angle$$DCB = 180$$^\circ$$

$$=$$> 94$$^\circ$$ + $$\angle$$DCB = 180$$^\circ$$

$$=$$> $$\angle$$DCB = 86$$^\circ$$

In the quadrilateral ABCD,

$$\angle$$ABF + $$\angle$$DCB + $$\angle$$CDA + $$\angle$$EAB = 360$$^\circ$$

$$=$$>  $$\angle$$ABF + 86$$^\circ$$ + 95$$^\circ$$ + $$\angle$$EAB = 360$$^\circ$$

$$=$$>  $$\angle$$ABF + $$\angle$$EAB + 181$$^\circ$$ = 360$$^\circ$$

$$=$$>  $$\angle$$ABF + $$\angle$$EAB = 179$$^\circ$$

Hence, the correct answer is Option B


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