In the figure shown above, $\mathrm{m} \angle Q$ measures $70^{\circ}, \overline{P Q} \cong \overline{P R}$, and $\overline{P Q}$ and $\overline{P R}$ are tangent to the circle with center $O$ at points $A$ and $B$. Find, in degrees, the measure of $\angle A O B$.

Step 1 ：The problem states that lines PQ and PR are tangent to the circle at points A and B respectively. This means that the lines OA and OB are perpendicular to PQ and PR respectively.

Step 2 ：Since PQ is congruent to PR, triangle POQ is congruent to triangle POR by SAS (Side-Angle-Side) congruence.

Step 3 ：This means that angle POQ is congruent to angle POR. Since angle Q measures 70 degrees, angle R also measures 70 degrees.

Step 4 ：The measure of angle AOB is then \(180 - 2*70 = 40\) degrees.

Step 5 ：Final Answer: The measure of \(\angle A O B\) is \(\boxed{40}\) degrees.