Solve for angle b in problem (10).

The two horizontal lines with arrows indicate they are parallel. The line intersecting them is a transversal. The angle $113^\circ$ and angle $b$ are consecutive interior angles. Consecutive interior angles are supplementary, meaning they add up to $180^\circ$.

$$113^\circ + b = 180^\circ$$

Subtract $113^\circ$ from both sides:

$$b = 180^\circ - 113^\circ$$ $$b = 67^\circ$$

The value of $b$ is $\boxed{\text{67}^\circ}$.

The diagram shows two intersecting lines. The angle $136^\circ$ and the angle adjacent to it on the straight line form a linear pair. A linear pair of angles are supplementary, meaning they add up to $180^\circ$. Angle $x$ is vertically opposite to this adjacent angle. Vertically opposite angles are equal.
First, find the angle adjacent to $136^\circ$:

$$180^\circ - 136^\circ = 44^\circ$$

Since $x$ is vertically opposite to this $44^\circ$ angle:

$$x = 44^\circ$$

The value of $x$ is $\boxed{\text{44}^\circ}$.

The two vertical lines with arrows indicate they are parallel. The line intersecting them is a transversal. The angle $81^\circ$ is an interior angle. The angle $y$ is an exterior angle.
The angle alternate interior to $81^\circ$ is the angle on the bottom parallel line, to the right of the transversal, inside the parallel lines. This angle is equal to $81^\circ$.
Angle $y$ and this alternate interior angle are vertically opposite angles. Vertically opposite angles are equal.
Therefore,

$$y = 81^\circ$$

The value of $y$ is $\boxed{\text{81}^\circ}$.