1. **State the problem:** We are given a circle with points Q, P, and R on its circumference. The angle at point P formed by chords QP and PR is 75°. 2. **Given:** The arc QP measures 80°. 3. **Goal:** Find the measure of the arc PR, which is indicated by a question mark. 4. **Key formula:** The measure of an inscribed angle is half the measure of its intercepted arc. $$\text{Inscribed angle} = \frac{1}{2} \times \text{Intercepted arc}$$ 5. **Apply the formula:** The angle at P intercepts the arc QR (the arc opposite to P between Q and R passing through the circle). Let the measure of arc QR be $x$. Then: $$75^\circ = \frac{1}{2} x \implies x = 2 \times 75^\circ = 150^\circ$$ 6. **Find arc PR:** The entire circle measures 360°. The arcs around the circle are QP (80°), PR (unknown), and QR (150°). Since QP + PR + QR = 360°, we have: $$80^\circ + \text{arc PR} + 150^\circ = 360^\circ$$ 7. **Solve for arc PR:** $$\text{arc PR} = 360^\circ - 80^\circ - 150^\circ = 130^\circ$$ **Final answer:** The measure of the arc PR is **130°**.