When an angle is bisected, two equal angles are created, and each of these new angles are equal to half the original angle.
So we have that:
[tex]\begin{gathered} \text{initial angle}=2\cdot\text{new angle} \\ 76=2\cdot\text{new angle} \\ \text{new angle}=\frac{76}{2}=38\degree \end{gathered}[/tex]
So the measure of both new angles is 38°.
