Part 1
Angles in a triangle add to 180 degrees, so
[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]
Part 2
By the Law of Sines,
[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]
