A side of the triangle below has been extended to form an exterior angle. What is the value of x.
+486 Let us denote the interior angle(not 114, not x) as y. Because the exterior angle plus the interior angle sum to $180^\circ$, we have $164+y=180$, which gives $y=16^\circ$. Now, we use the formula for the sum of the angles of a triangle. It states that the sum of all the angles in a triangle is equal to $180^\circ$, so we have $16+114+x=180$, which gives $x=180-16-114$, which gives $\boxed{x=50}$
+486 Let us denote the interior angle(not 114, not x) as y. Because the exterior angle plus the interior angle sum to $180^\circ$, we have $164+y=180$, which gives $y=16^\circ$. Now, we use the formula for the sum of the angles of a triangle. It states that the sum of all the angles in a triangle is equal to $180^\circ$, so we have $16+114+x=180$, which gives $x=180-16-114$, which gives $\boxed{x=50}$
