1. Stating the problem: We have two adjacent angles $\angle A$ and $\angle B$ such that $\angle B > \angle A$ and their ratio is $1:14$. We need to find the measures of $\angle A$ and $\angle B$. 2. Important rule: Adjacent angles formed by a straight line sum up to 180 degrees. So, $\angle A + \angle B = 180^\circ$. 3. Let $\angle A = x$. Then $\angle B = 14x$ because the ratio is 1:14. 4. Using the sum of adjacent angles: $$x + 14x = 180$$ $$15x = 180$$ 5. Solve for $x$: $$x = \frac{180}{15}$$ $$x = 12$$ 6. Calculate $\angle B$: $$\angle B = 14x = 14 \times 12 = 168$$ 7. Final answer: $\angle A = 12^\circ$ $\angle B = 168^\circ$