If the sum and difference of two angles are 135° and $$\frac{\pi }{{12}}$$  respectively, then the value of the angles in degree measure are?

Solution (By Examveda Team)

$$\eqalign{ & \angle {\text{A}} + \angle {\text{B}} = {135^ \circ }\,.....(i) \cr & \angle {\text{A}} - \angle {\text{B}} = \frac{\pi }{{12}} = {15^ \circ }\,.....(ii) \cr & Adding{\text{ both equations}} \cr & \Rightarrow 2\angle {\text{A}} = {150^ \circ } \cr & \Rightarrow \angle {\text{A}} = {75^ \circ } \cr & \therefore \angle {\text{B}} = {60^ \circ } \cr} $$