Answer:
[tex]x=80^{\circ}[/tex]
Step-by-step explanation:
Solution 1:
Recall that in an isosceles triangle, the two angles adjacent to the congruent sides are equal. Since the sum of interior angles in a triangle add up to [tex]180^{\circ}[/tex], we set up the following equation:
[tex]x+50+50=180[/tex].
Solving, we get:
[tex]x+100=80,\\x=\fbox{$80^{\circ}$}[/tex].
Solution 2:
The Law of Sines states:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex], for any triangle.
We can use this to set up a proportion with the information given:
[tex]\frac{\sin x}{18}=\frac{\sin 50^{\circ}}{14}[/tex].
Solving, we get:
[tex]x=\arcsin(\frac{18\cdot \sin 50^{\circ}}{14}),\\x \approx \fbox{$80^{\circ}$}[/tex].
