1. The problem states that $\angle Q$ and $\angle R$ are complementary angles. This means their measures add up to 90 degrees. 2. The formula for complementary angles is: $$\angle Q + \angle R = 90^\circ$$ 3. We are given that $\angle R = 26^\circ$. 4. Substitute $26^\circ$ for $\angle R$ in the formula: $$\angle Q + 26^\circ = 90^\circ$$ 5. To find $\angle Q$, subtract $26^\circ$ from both sides: $$\angle Q = 90^\circ - 26^\circ$$ 6. Simplify the right side: $$\angle Q = 64^\circ$$ 7. Therefore, the measure of $\angle Q$ is $64^\circ$.