worksheet on supplementary and complementary angles

Guri Bee

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22-10-2024

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Mastering Supplementary and Complementary Angles: A Worksheet Guide

Understanding supplementary and complementary angles is fundamental in geometry and trigonometry. This worksheet will help you solidify your knowledge by providing a series of exercises to test your grasp on the concepts.

What are Supplementary and Complementary Angles?

• Supplementary Angles: Two angles are supplementary if they add up to 180 degrees. Think of a straight line - it forms a 180-degree angle, and any two angles that make up that line are supplementary.
• Complementary Angles: Two angles are complementary if they add up to 90 degrees. Imagine a right angle - it forms a 90-degree angle, and any two angles that make up that right angle are complementary.

Worksheet: Putting Theory into Practice

This worksheet, inspired by this GitHub repository, offers a variety of exercises to test your understanding of supplementary and complementary angles.

1. Identifying Supplementary and Complementary Angles:

• Exercise 1:
  • Given two angles, ∠A = 110° and ∠B = 70°. Are these angles supplementary or complementary?
  • Solution: ∠A + ∠B = 110° + 70° = 180°. Therefore, ∠A and ∠B are supplementary angles.
• Exercise 2:
  • Two angles, ∠C = 45° and ∠D = 45°, form a right angle. Are these angles supplementary or complementary?
  • Solution: ∠C + ∠D = 45° + 45° = 90°. Therefore, ∠C and ∠D are complementary angles.

2. Finding Missing Angles:

• Exercise 3:
  • One angle measures 65°. What is the measure of its supplementary angle?
  • Solution: Let the supplementary angle be ∠x. We know that ∠x + 65° = 180°. Solving for ∠x, we get ∠x = 180° - 65° = 115°. The supplementary angle measures 115°.
• Exercise 4:
  • One angle measures 20°. What is the measure of its complementary angle?
  • Solution: Let the complementary angle be ∠y. We know that ∠y + 20° = 90°. Solving for ∠y, we get ∠y = 90° - 20° = 70°. The complementary angle measures 70°.

3. Word Problems:

• Exercise 5:
  • Two angles are supplementary. One angle is twice the size of the other. What is the measure of each angle?
  • Solution: Let the smaller angle be ∠x. The larger angle is 2∠x. Since they are supplementary, we have ∠x + 2∠x = 180°. Simplifying, we get 3∠x = 180°. Solving for ∠x, we get ∠x = 60°. The smaller angle is 60°, and the larger angle is 2(60°) = 120°.

Additional Tips:

• Visualize: Drawing diagrams for each problem can help you understand the relationships between the angles.
• Practice Makes Perfect: Don't hesitate to work through additional exercises to solidify your understanding.
• Real-Life Examples: Look for supplementary and complementary angles in your surroundings - the corner of a room, a pair of scissors, or a clock face.

By diligently working through these exercises, you will gain a strong foundation in understanding supplementary and complementary angles.