Answer
$\theta$ = 15$^{\circ}$
Work Step by Step
$\cos$(2$\theta$ + 50$^{\circ}$) = $\sin$(2$\theta$ - 20$^{\circ}$)
$\cos$ and $\sin$ are cofunctions if the sum of the angles is 90$^{\circ}$
Therefore:
(2$\theta$ + 50$^{\circ}$) + (2$\theta$ - 20$^{\circ}$) = 90$^{\circ}$
4$\theta$ + 30$^{\circ}$ = 90$^{\circ}$
4$\theta$ = 60$^{\circ}$
$\theta$ = 15$^{\circ}$
