When an angle is bisected, it is divided into two equal parts. In this case, the 80-degree angle is bisected.
To find the measure of each of the two smaller angles created, you can divide the measure of the original angle by 2:
\[ \frac{80 \text{ degrees}}{2} = 40 \text{ degrees} \]
Thus, the measure of each of the two smaller angles created is 40 degrees.