In a pie chart, if the corporate sector represents approximately $\frac{1}{3}\text{rd}$ ($34\%$) of the total data representation share, what should be the approximate number of degrees in its central angle?

A complete circle in a pie chart encompasses a total central angle of $360^{\circ }$, corresponding to $100\%$.
Given a corporate sector percentage share of approximately $34\%$ (or roughly $\frac{1}{3}\text{rd}$):

$$\text{Central Angle}=\frac{34}{100}\times 360^{\circ }$$

$$\text{Central Angle}=0.34\times 360^{\circ }=122.4^{\circ }\approx 122^{\circ }$$

Hence, the closest matching approximate integer degree value is $122^{\circ }$.