Answer
$\approx 153.2^0$
Work Step by Step
Lets find $\angle A$ Using law of sines
$\dfrac {3}{\sin 10}=\dfrac {5}{\sin \angle A}\Rightarrow \sin \angle A=\dfrac {5\times \sin 10}{3}\approx 029\Rightarrow \angle A\approx \sin ^{-1}\left( 0.29\right) \approx 16.8$
Sum of internal angles of a triangle is $180^0$
$10^{0}+\angle A+\theta =180^0\Rightarrow \theta =180^0-10^0-\angle A\approx 180^0-10^0-16.8^0\approx 153.2^0$
