From the figure, what is the value of x?

The correct option is 70^◦.

By analyzing the provided image, we can identify the following geometric features from triangle ABC:
1. The interior angle at vertex A is given as 50^◦.
2. The interior angle at vertex B is labeled as x.
3. The side BC is extended to a point D, which forms an exterior angle at vertex C, labeled as 120^◦.

To find the value of x, we can apply the Exterior Angle Theorem. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote (non-adjacent) interior angles.

Using the theorem, we can set up the following equation:

$$\angle ACD=\angle A+\angle B$$

Substitute the known values from the diagram into this relationship:

$$120°=50°+x$$

To isolate and solve for x, subtract 50° from both sides of the equation:

$$x=120°-50°$$

Calculate the final subtraction:

$$x=70°$$

Thus, the value of x is 70^◦.