1. **State the problem:** We have triangle ABC with interior angles at A and B given as 97° and 34°, respectively, and an exterior angle at vertex C labeled as $z$. We need to find the measure of the exterior angle $z$. 2. **Recall the exterior angle theorem:** The exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle $z$ at vertex C equals the sum of angles at A and B. 3. **Write the formula:** $$z = \angle A + \angle B$$ 4. **Substitute the known values:** $$z = 97^\circ + 34^\circ$$ 5. **Calculate the sum:** $$z = 131^\circ$$ 6. **Conclusion:** The measure of the exterior angle $z$ is $131^\circ$.