Answer
$α \approx 35^{\circ}$
$β \approx 55^{\circ}$
Work Step by Step
1. Find $α$
$tan = \frac{opposite}{adjacent}$
$tan(α) = \frac{\sqrt {3}}{\sqrt {6}}$
by GDC / calculator
$α = 35.26438...^{\circ}$
$α \approx 35^{\circ}$
2. Find $β$
$tan = \frac{opposite}{adjacent}$
$tan(β) = \frac{\sqrt {6}}{\sqrt {3}}$
by GDC / calculator
$β = 54.7356...^{\circ}$
$β \approx 55^{\circ}$