Complementary And Supplementary Angles Worksheet With Answers
Table of Contents :
Complementary and supplementary angles are essential concepts in geometry, often encountered in various mathematical problems. This article will explore these types of angles, provide a worksheet with examples, and offer answers to help solidify your understanding.
What Are Complementary Angles? 🤔
Complementary angles are two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, the complementary angle must measure 60 degrees, since:
30° + 60° = 90°
Properties of Complementary Angles
- Addition Property: The sum of complementary angles is always 90 degrees.
- Right Angle: Complementary angles create a right angle when combined.
- Geometric Representation: Complementary angles can exist in various geometric shapes, such as triangles and rectangles.
Examples of Complementary Angles
Here are a few examples of complementary angles:
- If Angle A = 45°, then Angle B = 90° - 45° = 45°.
- If Angle C = 30°, then Angle D = 90° - 30° = 60°.
What Are Supplementary Angles? 🤔
Supplementary angles are two angles whose measures add up to 180 degrees. For example, if one angle measures 110 degrees, the supplementary angle must measure 70 degrees since:
110° + 70° = 180°
Properties of Supplementary Angles
- Addition Property: The sum of supplementary angles is always 180 degrees.
- Straight Angle: Supplementary angles create a straight angle when combined.
- Geometric Representation: Supplementary angles frequently appear in parallel lines cut by a transversal.
Examples of Supplementary Angles
Here are a few examples of supplementary angles:
- If Angle E = 120°, then Angle F = 180° - 120° = 60°.
- If Angle G = 90°, then Angle H = 180° - 90° = 90°.
Complementary and Supplementary Angles Worksheet 📄
To practice your understanding of complementary and supplementary angles, here’s a worksheet that presents various angle measures. Complete the table by finding the missing angles.
<table> <tr> <th>Angle Measure</th> <th>Complementary Angle (C)</th> <th>Supplementary Angle (S)</th> </tr> <tr> <td>30°</td> <td></td> <td></td> </tr> <tr> <td>50°</td> <td></td> <td></td> </tr> <tr> <td>70°</td> <td></td> <td></td> </tr> <tr> <td>90°</td> <td></td> <td></td> </tr> <tr> <td>120°</td> <td></td> <td></td> </tr> <tr> <td>150°</td> <td></td> <td></td> </tr> </table>
Answers to the Worksheet ✔️
Now that you’ve completed the worksheet, here are the answers:
<table> <tr> <th>Angle Measure</th> <th>Complementary Angle (C)</th> <th>Supplementary Angle (S)</th> </tr> <tr> <td>30°</td> <td>60°</td> <td>150°</td> </tr> <tr> <td>50°</td> <td>40°</td> <td>130°</td> </tr> <tr> <td>70°</td> <td>20°</td> <td>110°</td> </tr> <tr> <td>90°</td> <td>0°</td> (or considered complementary to itself) <td>90°</td> </tr> <tr> <td>120°</td> <td>___ (Not applicable as it cannot have a complement)</td> <td>60°</td> </tr> <tr> <td>150°</td> <td>___ (Not applicable as it cannot have a complement)</td> <td>30°</td> </tr> </table>
Important Notes 🔍
- Complementary angles must always be less than or equal to 90 degrees.
- Supplementary angles can be any angles that add up to 180 degrees, which can include larger angles.
- Understanding the relationships between complementary and supplementary angles is crucial for solving many geometry problems.
Conclusion
Grasping the concepts of complementary and supplementary angles is fundamental for any geometry student. The provided worksheet allows for practice and reinforcement of these concepts. By learning to identify and calculate these angles, you'll develop a stronger foundation in geometry, beneficial for more advanced mathematical studies. Keep practicing, and don't hesitate to revisit the definitions and properties as you advance in your studies!