1. The problem states that two adjacent angles, $\angle A$ and $\angle B$, have a ratio of 1:5 and that $\angle B > \angle A$. We need to find the measures of these angles. 2. Since the angles are adjacent and form a straight line, their sum is $180^\circ$. So, $\angle A + \angle B = 180^\circ$. 3. Let $\angle A = x$. Then $\angle B = 5x$ because the ratio is 1:5. 4. Substitute into the sum equation: $$x + 5x = 180$$ 5. Simplify: $$6x = 180$$ 6. Solve for $x$: $$x = \frac{180}{6}$$ $$x = 30$$ 7. Therefore, $\angle A = 30^\circ$ and $\angle B = 5 \times 30 = 150^\circ$. 8. Check that $\angle B > \angle A$ and that their sum is $180^\circ$, which is true. Final answer: $\angle A = 30^\circ$, $\angle B = 150^\circ$.