Answer
$x = 7^{\circ}$
Work Step by Step
Use the concept of cofunction $\tan x = \cot (90^{\circ} -x)$
$\tan (5x +11^{\circ}) = \cot (6x +2^{\circ})$
$\tan (5x +11^{\circ}) = \tan (90^{\circ} - (6x +2^{\circ}))$
$5x +11 ^{\circ} = 90^{\circ} -6x -2^{\circ}$
$11x =77^{\circ}$
$x =7^{\circ}$
