Answer
$x \approx 10.9$
Work Step by Step
Apply the Law of Sines.
$\dfrac{\sin A}{a} =\dfrac{\sin B}{b} =\dfrac{\sin C}{c} $
Rearrange the first two ratio setup to obtain:
$\dfrac{\sin A}{10} =\dfrac{\sin 80^{\circ}}{x} \\ x=\dfrac{10 \sin 80^{\circ}}{\sin A} ~~~(1)$
Since, the sum of interior angles of a triangle is equal to $180^{\circ}$. Thus, we can write as:
$A+B+C =180^{\circ} \\ A+ 80^{\circ}+35^{\circ}=180^{\circ} \implies A = 65^{\circ}$
Hence, the equation (1) becomes:
$x=\dfrac{10 \sin 80^{\circ}}{\sin 65^{\circ}} \approx 10.9$
