Find α (Triangles)

Question

Find $\alpha$ if $A = 4\alpha$.

Can someone explain to me how to do this?

Answer 1

We know $A \hat{D}C = 90 \unicode{xb0}$ and we are given that $\hat{A}= 4 \alpha$.

Now, in triangle $ADC$, we require $$ 4\alpha + \alpha + 90\unicode{xb0}= 180 \unicode{xb0} \\ \therefore 5\alpha + 90 \unicode{xb0} = 180 \unicode{xb0}$$

All that is left now, is to solve for $\alpha$

\begin{align} 5\alpha &= 180 \unicode{xb0} - 90 \unicode{xb0}\\ \therefore5\alpha &= 90 \unicode{xb0} \\ \therefore \alpha &= 18 \unicode{xb0}\end{align}