Trigonometry 7th Edition

α = $30^{\circ}$
In given figure 21- $\angle$ CDB is right angle and ADB is a straight line, therefore $\angle$ CDA is also a right angle and hence triangle CDA is a right triangle. In right triangle CDA, C and A are acute angles, therefore- C + A = $90^{\circ}$ α + 2 α = $90^{\circ}$ ( Substituting values of C and A ) 3 α = $90^{\circ}$ α = $\frac{90^{\circ}}{3}$ = $30^{\circ}$