Complementary and Supplementary Angles Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Finding Complementary Angles", which asks students to find the value of \( x \) in each diagram such that the two angles shown form a right angle (90°). Since I can't view images directly, I’ll help you solve this type of problem based on the description and common patterns found in such worksheets.

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🔍 What Are Complementary Angles?

Two angles are complementary if their measures add up to 90 degrees.
So, if one angle is given as \( x \), and the other is expressed in terms of \( x \), we set up an equation:
\[
\text{Angle 1} + \text{Angle 2} = 90^\circ
\]

Let’s go through typical problems from such a worksheet.

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✔ Example Problems (Typical Format)

Assume the worksheet has diagrams like these:

#### Problem 1:
- One angle is labeled \( x \)
- The other angle is labeled \( 35^\circ \)
- They form a right angle

Then:
\[
x + 35^\circ = 90^\circ \\
x = 90^\circ - 35^\circ = 55^\circ
\]

✔ Answer: \( x = 55^\circ \)

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#### Problem 2:
- One angle is \( 2x \)
- The other is \( 40^\circ \)

Then:
\[
2x + 40^\circ = 90^\circ \\
2x = 50^\circ \\
x = 25^\circ
\]

✔ Answer: \( x = 25^\circ \)

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#### Problem 3:
- One angle is \( x \)
- The other is \( 6x \)

Then:
\[
x + 6x = 90^\circ \\
7x = 90^\circ \\
x = \frac{90}{7} \approx 12.86^\circ
\]

✔ Answer: \( x \approx 12.86^\circ \) (or leave as fraction: \( \frac{90}{7}^\circ \))

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#### Problem 4:
- One angle is \( 3x + 10^\circ \)
- The other is \( x + 20^\circ \)

Then:
\[
(3x + 10) + (x + 20) = 90 \\
4x + 30 = 90 \\
4x = 60 \\
x = 15
\]

✔ Answer: \( x = 15^\circ \)

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🧠 General Steps to Solve These Problems:

1. Identify the two angles in the diagram.
2. Set up an equation so that their sum equals 90°.
3. Solve for \( x \) using algebra.
4. Check your answer by plugging it back into the expressions.

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💡 Tips:

- Always ensure the total is 90° — not 180° (that’s supplementary).
- Look for variables like \( x \), \( 2x \), or expressions with constants.
- If the angles are adjacent and form a corner (like an "L"), they’re likely complementary.

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If you can describe the specific problems in your image (e.g., what angles are labeled), I can give you exact answers for each one.

For now, here’s a summary of how to approach any problem on this worksheet:

> Step-by-step method:
> 1. Add the two angles → Set equal to 90°
> 2. Combine like terms
> 3. Solve for \( x \)
> 4. Box your final answer

Let me know if you'd like help solving a specific diagram!