Answer
$\theta$ = 40$^{\circ}$
Work Step by Step
$\tan$ $\theta$ = $\cot$ ($\theta$ + 10$^{\circ}$)
According to Cofunction Identities
$\tan$ $\theta$ = $\cot$ ($\theta$ + 10$^{\circ}$) is true only if the sum of the angles is 90$^{\circ}$.
Therefore:
$\theta$ + ($\theta$ + 10$^{\circ}$) = 90$^{\circ}$
2$\theta$ + 10$^{\circ}$ = 90$^{\circ}$
2$\theta$ = 80$^{\circ}$
$\theta$ = 40$^{\circ}$
