Two angles of a triangle are $75^{\circ }$ and $45^{\circ }$. What is the value of the third angle in circular measure? (As per convention, do not use the symbol of radian.)

Let the third angle of the triangle be $x$.
The total sum of all interior angles inside any triangle is $180^{\circ }$.

$$75^{\circ }+45^{\circ }+x=180^{\circ }$$

$$120^{\circ }+x=180^{\circ }⟹x=60^{\circ }$$

To convert the degree angle into circular measure (radians), multiply by $\frac{\pi }{180^{\circ }}$:

$$\text{Circular Measure}=60^{\circ }\times \frac{\pi }{180^{\circ }}=\frac{\pi }{3}$$