The side BC of a triangle ABC is proceed to D. If ∠ACD = 112° and ∠B = 3/4 ∠A, then the measure of ∠B is:

Answer: Option C

Assume, ∠A = x
∴ ∠B = $$\frac{3}{4}$$ x
∠A + ∠B = 112° (∵ sum of two interior angle is equal to the exterior angle of the third angle)
$$\begin{array}{rl}& x^{\circ }+\frac{3}{4}{x}^{\circ }=112^{\circ }\\ & \frac{7x^{\circ }}{4}=112^{\circ }\\ & x^{\circ }=64^{\circ }\\ & \text{Hence,}\\ & \angle B=\frac{3}{4}\times 64^{\circ }\\ & \angle B=48^{\circ }\end{array}$$