# How do you answer this question?

May 1, 2018

$\Delta A D C$ is an isosceles right triangle

$\therefore$

$\angle A D C = {45}^{\circ}$

$\angle A C B = {60}^{\circ}$ because is it one of the 3 angles of an equilateral triangle.

$\therefore$

$\angle D C B = {90}^{\circ} + {60}^{\circ} = {150}^{\circ}$

Because $\angle B D C$ is opposite one of two equal sides of $\Delta B D C$:

$\angle B D C = \frac{{180}^{\circ} - \angle D C B}{2}$

$\angle B D C = \frac{{180}^{\circ} - {150}^{\circ}}{2}$

$\angle B D C = {15}^{\circ}$

$\angle A D B = \angle A D C - \angle B D C$

$\angle A D B = {45}^{\circ} - {15}^{\circ}$

$\angle A D B = {30}^{\circ}$ Q.E.D.

May 1, 2018

.