**Problem Analysis**

Let's analyze the given information:

- We have a circle with center O.
- From an external point P, tangents PA and PB are drawn to the circle.
- We are given that angle PAB is 50 degrees.

We need to find angle AOB, which is the angle formed by the lines OA and OB at the center of the circle.

**Solution**

To find angle AOB, we need to understand the properties of tangents and angles in a circle:

1. The tangent to a circle is perpendicular to the radius drawn to the point of tangency.
2. The angle between a tangent and a chord drawn from the point of contact is equal to half the angle subtended by the chord at the center.

**Applying the Properties**

Let's apply the above properties to solve the problem:

1. Since PA and PB are tangents to the circle, they are perpendicular to the radii OA and OB, respectively.
2. Angle PAB is subtended by chord AB at the center O. Therefore, angle AOB is twice the measure of angle PAB.
3. We are given that angle PAB is 50 degrees. Therefore, angle AOB = 2 * 50 = 100 degrees.

**Answer**

The measure of angle AOB is 100 degrees.

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