1. The problem asks to find the value of angle $r$ given that it forms a linear pair with an angle of $69.1^\circ$. 2. Recall that angles forming a linear pair are supplementary, meaning their measures add up to $180^\circ$. 3. The formula for supplementary angles is: $$r + 69.1^\circ = 180^\circ$$ 4. To find $r$, subtract $69.1^\circ$ from both sides: $$r = 180^\circ - 69.1^\circ$$ 5. Calculate the difference: $$r = 110.9^\circ$$ 6. Therefore, the value of $r$ is $110.9^\circ$.