Answer key for a math worksheet with addition and subtraction exercises.

The image you uploaded appears to be a math worksheet titled "Common Complementary Angles," which involves finding the complementary angles for given angles. Here's how to solve such problems and explain the solution:

Understanding Complementary Angles

- Two angles are complementary if their measures add up to 90 degrees.
- If one angle is \( x \), then its complement is \( 90^\circ - x \).

Steps to Solve the Problem

1. Identify the given angle in each row.
2. Subtract the given angle from 90 degrees to find its complement.
3. Write the result in the corresponding box.

Example Calculation

Let’s take a few examples from the worksheet:

#### Example 1:
- Given angle: \( 85^\circ \)
- Complement: \( 90^\circ - 85^\circ = 5^\circ \)

#### Example 2:
- Given angle: \( 70^\circ \)
- Complement: \( 90^\circ - 70^\circ = 20^\circ \)

#### Example 3:
- Given angle: \( 45^\circ \)
- Complement: \( 90^\circ - 45^\circ = 45^\circ \)

General Formula

For any given angle \( x \):
\[
\text{Complement} = 90^\circ - x
\]

Worksheet Solution

Here is the completed worksheet with all the answers filled in:

| Given Angle | Complement |
|-------------|------------|
| 85 | 5 |
| 70 | 20 |
| 45 | 45 |
| 90 | 0 |
| 10 | 80 |
| 80 | 10 |
| 15 | 75 |
| 60 | 30 |
| 75 | 15 |
| 30 | 60 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |
| 90 | 0 |

Final Answer

The completed worksheet is as follows:

\[
\boxed{
\begin{array}{c|c}
\text{Given Angle} & \text{Complement} \\
\hline
85 & 5 \\
70 & 20 \\
45 & 45 \\
90 & 0 \\
10 & 80 \\
80 & 10 \\
15 & 75 \\
60 & 30 \\
75 & 15 \\
30 & 60 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
90 & 0 \\
\end{array}
}
\]

This ensures that each pair of angles adds up to 90 degrees, fulfilling the definition of complementary angles.