1. **State the problem:** We are given a diagram with angles 27° and 112° and need to find the angle $x$ formed between lines $OC$ and $OP$. 2. **Identify relationships:** The points and angles suggest that the lines form a full circle around point $O$, so the sum of all angles around $O$ is 360°. 3. **Use the angle sum rule:** The angles around point $O$ add up to 360°, so $$27^\circ + 112^\circ + x + \text{other angles} = 360^\circ.$$ 4. **Assuming the other angles are the same as the given 27° and 112° (since the problem implies symmetry or complementary angles), the sum of the known angles is $$27^\circ + 112^\circ = 139^\circ.$$ 5. **Calculate $x$ by subtracting the known angles from 360°:** $$x = 360^\circ - 139^\circ = 221^\circ.$$ 6. **Check if $x$ is the reflex angle or the smaller angle:** Usually, $x$ is the smaller angle between the lines, so we take the supplementary angle: $$x = 360^\circ - 221^\circ = 139^\circ.$$ 7. **Final answer:** $$\boxed{139^\circ}$$