In a ΔABC, if 4∠A = 3∠B = 12∠C, find ∠A?

Solution (By Examveda Team)

$$\eqalign{ & {\text{4}}\angle {\text{A}} = {\text{3}}\angle {\text{B}} = {\text{12}}\angle {\text{C}} \cr & {\text{A}}:{\text{B}}:{\text{C}} = \frac{1}{4}:\frac{1}{3}:\frac{1}{{12}} \cr & {\text{A}}:{\text{B}}:{\text{C}} = 3:4:1 \cr & {\text{Now,}} \cr & 3x + 4x + x = {180^ \circ } \cr & 8x = {180^ \circ } \cr & x = \frac{{{{180}^ \circ }}}{8} \cr & \angle {\text{A}} = 3x = \frac{{{{180}^ \circ }}}{8} \times 3 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {67.5^ \circ } \cr} $$