Solve for the marked angles in the provided figures.

The angles $72^\circ$, $56^\circ$, and $f$ are the interior angles of the top triangle. The sum of angles in a triangle is $180^\circ$.

$$72^\circ + 56^\circ + f = 180^\circ$$ $$128^\circ + f = 180^\circ$$ $$f = 180^\circ - 128^\circ$$ $$f = 52^\circ$$

The value of $f$ is $\boxed{\text{52}^\circ}$.

Angle $z$ and the exterior angle $107^\circ$ are angles on a straight line, so their sum is $180^\circ$.

$$z + 107^\circ = 180^\circ$$ $$z = 180^\circ - 107^\circ$$ $$z = 73^\circ$$

Now, use the sum of angles in the triangle: $y + 50^\circ + z = 180^\circ$.

$$y + 50^\circ + 73^\circ = 180^\circ$$ $$y + 123^\circ = 180^\circ$$ $$y = 180^\circ - 123^\circ$$ $$y = 57^\circ$$

The values are $y = \boxed{\text{57}^\circ}$ and $z = \boxed{\text{73}^\circ}$.

The interior angle $4x$ and the exterior angle $5x$ are angles on a straight line, so their sum is $180^\circ$.

$$4x + 5x = 180^\circ$$ $$9x = 180^\circ$$ $$x = \frac{180^\circ}{9}$$ $$x = 20^\circ$$

Now, use the sum of angles in the triangle: $a + 3x + 4x = 180^\circ$.

$$a + 3(20^\circ) + 4(20^\circ) = 180^\circ$$ $$a + 60^\circ + 80^\circ = 180^\circ$$ $$a + 140^\circ = 180^\circ$$ $$a = 180^\circ - 140^\circ$$ $$a = 40^\circ$$

The values are $x = \boxed{\text{20}^\circ}$ and $a = \boxed{\text{40}^\circ}$.

The interior angle adjacent to the exterior angle $120^\circ$ is $180^\circ - 120^\circ = 60^\circ$.
Now, use the sum of angles in the triangle: $c + 39^\circ + 60^\circ = 180^\circ$.

$$c + 99^\circ = 180^\circ$$ $$c = 180^\circ - 99^\circ$$ $$c = 81^\circ$$

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

In the top triangle, the sum of angles is $180^\circ$.

$$e + 50^\circ + 38^\circ = 180^\circ$$ $$e + 88^\circ = 180^\circ$$ $$e = 180^\circ - 88^\circ$$ $$e = 92^\circ$$

Angle $d$ is vertically opposite to the $38^\circ$ angle in the top triangle, or we can use the sum of angles in the bottom triangle. The interior angle adjacent to the exterior angle $130^\circ$ is $180^\circ - 130^\circ = 50^\circ$.
In the bottom triangle, the angles are $d$, $e$ (which is $92^\circ$), and $50^\circ$.

$$d + 92^\circ + 50^\circ = 180^\circ$$ $$d + 142^\circ = 180^\circ$$ $$d = 180^\circ - 142^\circ$$ $$d = 38^\circ$$

The values are $d = \boxed{\text{38}^\circ}$ and $e = \boxed{\text{92}^\circ}$.

This is a right-angled triangle, so one angle is $90^\circ$. The sum of angles in a triangle is $180^\circ$.

$$g + 90^\circ + 47^\circ = 180^\circ$$ $$g + 137^\circ = 180^\circ$$ $$g = 180^\circ - 137^\circ$$ $$g = 43^\circ$$

The value of $g$ is $\boxed{\text{43}^\circ}$.