In triangle $ABC$ shown above, the measures of angles $A$ and $C$ are each $50^{\circ}$, and the measure of angle $B$ is $x^{\circ}$. What is the value of $x$?

The interior angles of any triangle sum to $180^{\circ}$: $50 + 50 + x = 180 \Rightarrow x = 80$. The figure also lets you confirm that the triangle is isosceles — the two $50^{\circ}$ angles are at the base, and the side $AB$ opposite angle $C$ equals the side $BC$ opposite angle $A$. The apex angle $B$ is the one we are solving for. Trap A ($50$) mistakes the isosceles property — that the *base* angles are equal — for *all* angles being equal (which would require an equilateral triangle with $60^{\circ}$ each, option B).