1. **Stating the problem:** We have a triangle inscribed in a circle with two known angles: one is 70° adjacent to side $n$, and another is 50°. We need to find the measure of angle $m$ inside the triangle. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. That is, $$m + 70^\circ + 50^\circ = 180^\circ$$ 3. **Calculate angle $m$:** $$m = 180^\circ - 70^\circ - 50^\circ$$ 4. **Simplify:** $$m = 180^\circ - 120^\circ$$ $$m = 60^\circ$$ 5. **Conclusion:** The measure of angle $m$ is $60^\circ$. This uses the fundamental property of triangles and does not require additional circle theorems since the triangle's interior angles sum to 180° regardless of the circle.