Step 1: Understand the Geometry of Tangents and Radii.
When two tangents are drawn to a circle from an external point, the angle between the tangents is related to the angle between the radii drawn to the points of tangency. The relationship is given by:
$$
\text{Angle between tangents} = 180^\circ - \text{Angle between radii}.
$$
Step 2: Apply the Relationship.
Given that the angle between the tangents is $ 50^\circ $, we can use the formula:
$$
\text{Angle between radii} = 180^\circ - \text{Angle between tangents}.
$$
Substitute the given angle:
$$
\text{Angle between radii} = 180^\circ - 50^\circ = 130^\circ.
$$
Step 3: Analyze the Options.
Option (1): $ 150^\circ $ — Incorrect, as this does not match the calculated value.
Option (2): $ 140^\circ $ — Incorrect, as this does not match the calculated value.
Option (3): $ 130^\circ $ — Correct, as it matches the calculated value.
Option (4): $ 120^\circ $ — Incorrect, as this does not match the calculated value.
Step 4: Final Answer.
$$
(3) \mathbf{130^\circ}
$$