A3 How many degrees does the angle $\alpha$ measure, if the sum of its complementary and supplementary angles is equal to $4 \alpha$?
(A) $15^{\circ}$
(B) $30^{\circ}$
(C) $45^{\circ}$
(D) $60^{\circ}$
(E) $25^{\circ}$
A3. The complementary angle of angle $\alpha$ is $90^{\circ}-\alpha$. The supplementary angle of angle $\alpha$ is $180^{\circ}-\alpha$. The sum of these two angles is $90^{\circ}-\alpha+180^{\circ}-\alpha$. We add $270^{\circ}-2 \alpha$ and set it equal to $4 \alpha$. We get the equation $4 \alpha=270^{\circ}-2 \alpha$. The equation has the solution $\alpha=45^{\circ}$.