Answer
$\theta$ = 20$^{\circ}$
Work Step by Step
$\sin$ (2$\theta$ + 10$^{\circ}$) = $\cos$ (3$\theta$ - 20$^{\circ}$)
According to Cofunction Identities
$\sin$ (2$\theta$ + 10$^{\circ}$) = $\cos$ (3$\theta$ - 20$^{\circ}$) is true only if the sum of the angles is 90$^{\circ}$.
Therefore:
(2$\theta$ + 10$^{\circ}$) + (3$\theta$ - 20$^{\circ}$) = 90$^{\circ}$
5$\theta$ - 10$^{\circ}$ = 90$^{\circ}$
5$\theta$ = 100$^{\circ}$
$\theta$ = 20$^{\circ}$
