Find the value of x in each geometric figure involving angles and polygons.

To solve for \( x \) in each of the given problems, we will analyze each diagram step by step using geometric properties such as the sum of angles in a triangle, supplementary angles, and other relevant angle relationships.

---

Problem 1:

The first diagram shows a triangle with angles labeled as \( (3x)^\circ \), \( (2x)^\circ \), and \( (3x)^\circ \). The exterior angle adjacent to one of the \( (3x)^\circ \) angles is given as \( 160^\circ \).

#### Step 1: Use the property of exterior angles.
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore:
\[
160^\circ = (2x) + (3x)
\]
\[
160^\circ = 5x
\]

#### Step 2: Solve for \( x \).
\[
x = \frac{160}{5} = 32
\]

#### Final Answer for Problem 1:
\[
\boxed{32}
\]

---

Problem 2:

The second diagram shows a quadrilateral with angles labeled as \( (3x)^\circ \), \( (2x)^\circ \), \( (3x)^\circ \), and an unknown angle. The quadrilateral has a right angle (90°).

#### Step 1: Use the sum of interior angles of a quadrilateral.
The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
(3x) + (2x) + (3x) + 90^\circ = 360^\circ
\]
\[
8x + 90^\circ = 360^\circ
\]

#### Step 2: Solve for \( x \).
\[
8x = 270^\circ
\]
\[
x = \frac{270}{8} = 33.75
\]

#### Final Answer for Problem 2:
\[
\boxed{33.75}
\]

---

Problem 3:

The third diagram shows a quadrilateral with angles labeled as \( (100 - x)^\circ \), \( x \), \( 65^\circ \), and \( (90 - \frac{x}{2})^\circ \).

#### Step 1: Use the sum of interior angles of a quadrilateral.
The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
(100 - x) + x + 65 + \left(90 - \frac{x}{2}\right) = 360
\]
\[
100 - x + x + 65 + 90 - \frac{x}{2} = 360
\]
\[
255 - \frac{x}{2} = 360
\]

#### Step 2: Solve for \( x \).
\[
-\frac{x}{2} = 360 - 255
\]
\[
-\frac{x}{2} = 105
\]
\[
x = -210
\]

#### Final Answer for Problem 3:
\[
\boxed{-210}
\]

---

Problem 4:

The fourth diagram shows a quadrilateral with angles labeled as \( (x + 30)^\circ \), \( (7x)^\circ \), \( (31x)^\circ \), and \( (8x - 25)^\circ \).

#### Step 1: Use the sum of interior angles of a quadrilateral.
The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore:
\[
(x + 30) + (7x) + (31x) + (8x - 25) = 360
\]
\[
x + 30 + 7x + 31x + 8x - 25 = 360
\]
\[
47x + 5 = 360
\]

#### Step 2: Solve for \( x \).
\[
47x = 355
\]
\[
x = \frac{355}{47} = 7.553
\]

#### Final Answer for Problem 4:
\[
\boxed{7.553}
\]

---

Problem 5:

The fifth diagram shows a pentagon with angles labeled as \( \left(\frac{4}{3}x\right)^\circ \), \( \left(\frac{4}{5}x\right)^\circ \), \( \left(2x - 70\right)^\circ \), \( \left(178 - \frac{x}{5}\right)^\circ \), and \( \left(120 + \frac{1}{3}x\right)^\circ \).

#### Step 1: Use the sum of interior angles of a pentagon.
The sum of the interior angles of a pentagon is \( 540^\circ \). Therefore:
\[
\left(\frac{4}{3}x\right) + \left(\frac{4}{5}x\right) + \left(2x - 70\right) + \left(178 - \frac{x}{5}\right) + \left(120 + \frac{1}{3}x\right) = 540
\]

#### Step 2: Combine like terms.
First, combine the \( x \)-terms:
\[
\frac{4}{3}x + \frac{4}{5}x + 2x - \frac{x}{5} + \frac{1}{3}x
\]
Find a common denominator (15):
\[
\frac{20}{15}x + \frac{12}{15}x + \frac{30}{15}x - \frac{3}{15}x + \frac{5}{15}x = \frac{64}{15}x
\]

Next, combine the constant terms:
\[
-70 + 178 + 120 = 228
\]

So the equation becomes:
\[
\frac{64}{15}x + 228 = 540
\]

#### Step 3: Solve for \( x \).
\[
\frac{64}{15}x = 540 - 228
\]
\[
\frac{64}{15}x = 312
\]
\[
x = 312 \cdot \frac{15}{64}
\]
\[
x = \frac{4680}{64} = 73.125
\]

#### Final Answer for Problem 5:
\[
\boxed{73.125}
\]

---

Final Answers:

1. \(\boxed{32}\)
2. \(\boxed{33.75}\)
3. \(\boxed{-210}\)
4. \(\boxed{7.553}\)
5. \(\boxed{73.125}\)