Answer
$α \approx 29^{\circ}$
$β \approx 61^{\circ}$
Work Step by Step
1. Find $α$
$tan = \frac{opposite}{adjacent}$
$tan(α) = \frac{\sqrt {5}}{4}$
by GDC / calculator
$α = 29.20593...^{\circ}$
$α \approx 29^{\circ}$
2. Find $β$
$tan = \frac{opposite}{adjacent}$
$tan(β) = \frac{4}{\sqrt {5}}$
by GDC / calculator
$β = 60.79406...^{\circ}$
$β \approx 61^{\circ}$
