#### Answer

$\theta = 30^{\circ}$

#### Work Step by Step

Use the concept of cofunctions $\sin x = \cos (90^{\circ} - x)$
$\cos (\frac{3\theta}{5} + 11^{\circ}) = \sin (\frac{7\theta}{10}+40^{\circ})$
$\cos (\frac{3\theta}{5} + 11^{\circ}) = \cos (90^{\circ} -\frac{7\theta}{10} -40^{\circ})$
$\frac{3\theta}{5} + 11^{\circ} = 90^{\circ} -\frac{7\theta}{10} -40^{\circ} $
$\frac{13\theta}{10} = 39^{\circ}$
$\theta = 30^{\circ}$