Answer
$\alpha=53.1$
$\beta=36.9$
$\phi=53.1$
$\theta=36.9$
Work Step by Step
$6^{2}+8^{2}=DB^{2}$
$36+64=DB^{2}$
$DB^{2}=100$
$DB=10$
$\cos\alpha=\frac{6}{10}$
$\alpha=\cos^{-1}\frac{6}{10}$
$\alpha=53.1$
$\cos\theta=\frac{8}{10}$
$\theta=\cos^{-1}\frac{8}{10}$
$\theta=36.9$
Because $\overline{AD}$ is parallel to $\overline{BC}$, this means $\theta = \beta$ and $\alpha=\phi$ as they are alternating angles.
$\alpha=\phi=53.1$
$\theta=\beta=36.9$
