ABCD is a cyclic quadrilateral such that when sides AB and DC are produced, they meet at E, and sides AD and BC meet at F, when produced. If $$\angle$$ADE = 80$$^\circ$$ and $$\angle$$AED = 50$$^\circ$$, then what is the measure of $$\angle$$AFB?

From triangle AED,

$$\angle$$ADE + $$\angle$$AED + $$\angle$$DAE = 180$$^\circ$$

80$$^\circ$$ + 50$$^\circ$$ + $$\angle$$DAE = 180$$^\circ$$

$$\angle$$DAE = 50$$^\circ$$

ABCD is a cyclic quadrilateral.

Opposite angles in a cyclic quadrilateral is supplementary.

$$\angle$$ADC + $$\angle$$ABC = 180$$^\circ$$

80$$^\circ$$ + $$\angle$$ABC = 180$$^\circ$$

$$\angle$$ABC = 100$$^\circ$$

From triangle ABF,

$$\angle$$ABF + $$\angle$$AFB + $$\angle$$BAF = 180$$^\circ$$

100$$^\circ$$ + $$\angle$$AFB + 50$$^\circ$$ = 180$$^\circ$$

$$\angle$$AFB = 30$$^\circ$$

Hence, the correct answer is Option D