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To solve the problem of finding the angle (in degrees) of the shaded portion of each circle, we need to follow these steps:

Step-by-Step Solution:

1. Understand the Total Angle in a Circle:
- A full circle is always 360 degrees.

2. Determine the Number of Equal Parts:
- Each circle is divided into equal parts. Count how many equal parts each circle is divided into.

3. Calculate the Angle for Each Part:
- If a circle is divided into \( n \) equal parts, then each part represents an angle of:
\[
\text{Angle per part} = \frac{360^\circ}{n}
\]

4. Count the Shaded Parts:
- Determine how many of these equal parts are shaded.

5. Calculate the Total Shaded Angle:
- Multiply the angle per part by the number of shaded parts:
\[
\text{Total shaded angle} = (\text{Angle per part}) \times (\text{Number of shaded parts})
\]

Applying the Steps to Each Circle:

#### 1)
- Total parts: 4
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{4} = 90^\circ \)
- Total shaded angle: \( 90^\circ \times 1 = 90^\circ \)

#### 2)
- Total parts: 4
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{4} = 90^\circ \)
- Total shaded angle: \( 90^\circ \times 1 = 90^\circ \)

#### 3)
- Total parts: 8
- Shaded parts: 2
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 2 = 90^\circ \)

#### 4)
- Total parts: 3
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{3} = 120^\circ \)
- Total shaded angle: \( 120^\circ \times 1 = 120^\circ \)

#### 5)
- Total parts: 4
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{4} = 90^\circ \)
- Total shaded angle: \( 90^\circ \times 1 = 90^\circ \)

#### 6)
- Total parts: 4
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{4} = 90^\circ \)
- Total shaded angle: \( 90^\circ \times 1 = 90^\circ \)

#### 7)
- Total parts: 8
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 1 = 45^\circ \)

#### 8)
- Total parts: 8
- Shaded parts: 2
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 2 = 90^\circ \)

#### 9)
- Total parts: 3
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{3} = 120^\circ \)
- Total shaded angle: \( 120^\circ \times 1 = 120^\circ \)

#### 10)
- Total parts: 4
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{4} = 90^\circ \)
- Total shaded angle: \( 90^\circ \times 1 = 90^\circ \)

#### 11)
- Total parts: 8
- Shaded parts: 2
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 2 = 90^\circ \)

#### 12)
- Total parts: 8
- Shaded parts: 3
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 3 = 135^\circ \)

#### 13)
- Total parts: 8
- Shaded parts: 2
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 2 = 90^\circ \)

#### 14)
- Total parts: 6
- Shaded parts: 1
- Angle per part: \( \frac{360^\circ}{6} = 60^\circ \)
- Total shaded angle: \( 60^\circ \times 1 = 60^\circ \)

#### 15)
- Total parts: 8
- Shaded parts: 3
- Angle per part: \( \frac{360^\circ}{8} = 45^\circ \)
- Total shaded angle: \( 45^\circ \times 3 = 135^\circ \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 90^\circ \\
2) & 90^\circ \\
3) & 90^\circ \\
4) & 120^\circ \\
5) & 90^\circ \\
6) & 90^\circ \\
7) & 45^\circ \\
8) & 90^\circ \\
9) & 120^\circ \\
10) & 90^\circ \\
11) & 90^\circ \\
12) & 135^\circ \\
13) & 90^\circ \\
14) & 60^\circ \\
15) & 135^\circ \\
\end{array}
}
\]