1. **Stating the problem:** We have a circle centered at point P with two arcs: one arc IJ measuring 36° and another arc LK measuring 160°. We want to analyze these arcs and their properties. 2. **Formula and rules:** The total degrees in a circle is 360°. The sum of the arcs around the circle must equal 360°. 3. **Calculate the remaining arc:** $$\text{Remaining arc} = 360^\circ - (36^\circ + 160^\circ) = 360^\circ - 196^\circ = 164^\circ$$ 4. **Interpretation:** The circle is divided into three arcs: 36°, 160°, and 164°. 5. **Additional info:** The radius length is given as 12.77 units, which can be used to find arc lengths if needed using the formula: $$\text{Arc length} = r \times \theta$$ where $\theta$ is in radians. 6. **Convert degrees to radians:** $$\theta_{36} = 36^\circ \times \frac{\pi}{180} = \frac{\pi}{5}$$ $$\theta_{160} = 160^\circ \times \frac{\pi}{180} = \frac{8\pi}{9}$$ 7. **Calculate arc lengths:** $$\text{Arc length}_{36} = 12.77 \times \frac{\pi}{5} \approx 8.02$$ $$\text{Arc length}_{160} = 12.77 \times \frac{8\pi}{9} \approx 35.68$$ **Final answer:** The arcs measure 36°, 160°, and 164° respectively, with arc lengths approximately 8.02 and 35.68 units for the 36° and 160° arcs.