The side BC of a triangle ABC is extended to the point D. If $$\angle$$ACD = $$132^\circ$$ and $$\angle$$B = $$\frac{4}{7} \angle$$A, then the measure of $$\angle$$A is

Given, $$\angle$$ACD = $$132^\circ$$  and  $$\angle$$B = $$\frac{4}{7} \angle$$A

In $$\triangle$$ABC,

$$\angle$$ACD is the external angle at C which is equal to the sum of opposite angles A and B.

$$\Rightarrow$$  $$\angle$$ACD = $$\angle$$A + $$\angle$$B

$$\Rightarrow$$  $$132^\circ$$ = $$\angle$$A + $$\frac{4}{7} \angle$$A

$$\Rightarrow$$  $$132^\circ$$ = $$\frac{11}{7} \angle$$A

$$\Rightarrow$$  $$\angle$$A = $$84^\circ$$

Hence, the correct answer is Option C