Grade 5
  1. Number Sense and Place Value  1.1. Understanding Large Numbers  1.2. Place Value up to Millions  1.3. Comparing and Ordering Numbers  1.4. Rounding Whole Numbers  1.5. Expanded Form and Standard Form  1.6. Estimation in Calculations
  2. Operations with Whole Numbers  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Multiplication Concepts and Strategies  2.4. Division Concepts and Strategies  2.5. Multi-Digit Multiplication  2.6. Long Division  2.7. Order of Operations
  3. Fractions  3.1. Introduction to Fractions  3.2. Equivalent Fractions  3.3. Simplifying Fractions  3.4. Comparing and Ordering Fractions  3.5. Addition and Subtraction of Fractions  3.6. Multiplication of Fractions  3.7. Division of Fractions  3.8. Mixed Numbers and Improper Fractions  3.9. Converting Between Improper Fractions and Mixed Numbers
  4. Decimals  4.1. Understanding Decimals  4.2. Place Value in Decimals  4.3. Comparing and Ordering Decimals  4.4. Rounding Decimals  4.5. Addition and Subtraction of Decimals  4.6. Multiplication of Decimals  4.7. Division of Decimals  4.8. Converting Decimals to Fractions and Vice Versa
  5. Measurement  5.1. Length Measurement (Metric and Customary Units)  5.2. Weight and Mass Measurement  5.3. Volume and Capacity Measurement  5.4. Area of Squares and Rectangles  5.5. Perimeter of Polygons  5.6. Time and Elapsed Time  5.7. Temperature  5.8. Understanding Metric Conversions
  6. Geometry  6.1. Types of Lines and Angles  6.2. Measuring Angles  6.3. Classifying Triangles  6.4. Properties of Quadrilaterals  6.5. Symmetry and Reflection  6.6. Transformations (Translation, Rotation, Reflection)  6.7. Coordinate Plane and Plotting Points  6.8. 3D Shapes and Their Properties  6.9. Nets of 3D Shapes  6.10. Understanding Congruence and Similarity
  7. Data and Probability  7.1. Introduction to Data Collection  7.2. Organizing Data (Tables and Tally Charts)  7.3. Graphs (Bar Graphs, Line Plots, Pictographs)  7.4. Mean, Median, and Mode  7.5. Range of Data  7.6. Introduction to Probability  7.7. Simple Events and Outcomes  7.8. Probability of Independent Events
  8. Ratios and Proportions  8.1. Understanding Ratios  8.2. Writing and Simplifying Ratios  8.3. Equivalent Ratios  8.4. Introduction to Proportions  8.5. Solving Proportion Problems
  9. Algebraic Thinking  9.1. Understanding Variables and Expressions  9.2. Writing Algebraic Expressions  9.3. Simplifying Expressions  9.4. Solving One-Step Equations  9.5. Understanding Patterns and Sequences  9.6. Using the Distributive Property
  10. Financial Literacy  10.1. Introduction to Money and Currency  10.2. Budgeting Basics  10.3. Saving and Spending  10.4. Understanding Interest  10.5. Basic Financial Planning  10.6. Simple vs. Compound Interest

Grade 5 → Geometry ↓


Measuring Angles


Let's explore the wonderful world of angles. Angles are a fundamental concept in geometry and are important in understanding shapes, patterns and the world around us. This lesson will take you on a journey to understand and measure angles in a simple and fun way.

What is the angle?

An angle is formed when two lines or line segments meet or intersect at a common point. This intersection forms an opening, which we call an angle. The point where they meet is known as the vertex, and the lines are called the sides or arms of the angle.

ABPeak

In the above illustration, the angle is formed by lines meeting at the vertex.

Parts of an angle

  • Vertex: The common point at which two lines meet.
  • Sides: Lines that form angles.
  • Interior: The space between the arms.

Types of angles

Depending on the amount of rotation between the sides, angles are classified into different types. Let's take a look at some of the common types:

Acute angle

An acute angle is an angle that measures less than 90 degrees. Imagine a slice of pizza cut too wide.

less than 90°

Right angle

A right angle measures exactly 90 degrees. It is like the corner of a square or rectangle.

90°

Obtuse angle

An obtuse angle measures more than 90 degrees but less than 180 degrees. Think of an umbrella that's slightly open.

More than 90°

Straight angle

A straight angle is exactly 180 degrees. It's like a straight line.

180°

Reflex angle

The reflex angle is more than 180 degrees but less than 360 degrees. This is equivalent to more than half a revolution of a windmill blade.

More than 180°

Measuring angles

To measure angles we use a tool called a protractor. The protractor helps us to measure angles in degrees.

How to use a protractor

  1. Place the protractor: Align the midpoint of the protractor with the vertex of the angle.
  2. Align the baseline: Make sure one side of the angle is along the baseline of the protractor, which is usually the 0-degree line.
  3. Read the measurement: Where the other arm crosses the number scale on the protractor, that number is the measure of the angle.

Example: Measuring angles

Let's say one arm on the protractor makes an angle of 0 degrees, as shown in the figure.

45°

The angle is 45 degrees, depending on where the side crosses the number scale.

Uses of angles in real life

Angles are not just a part of geometry classes; we encounter them in a variety of everyday activities. For example:

  • Construction: Builders use angles in designing and building buildings.
  • Art: Artists use angles to create perspective in their works.
  • Navigation: Pilots and captains use angles to determine flight and sea routes.

Angle relationships

We often come across angles that interact with each other. Understanding their relationship helps in solving various geometric problems.

Supplementary angles

Two angles are said to be complementary if the sum of their measures is 90 degrees.

Angle 1 + Angle 2 = 90°

For example, 30 degrees and 60 degrees are complementary angles because they sum to 90 degrees.

Obtuse angle

Two angles are supplementary if the sum of their measures is 180 degrees.

Angle 1 + Angle 2 = 180°

For example, 110 degrees and 70 degrees are complementary angles because they sum to 180 degrees.

Vertical angles

When two lines cross each other, they form two pairs of opposite (or vertical) angles. These angles are always equal.

If two intersecting lines form an angle of 120 degrees, then the opposite angle will also be 120 degrees.

Playing with angles

Now, let's do some exercises to understand angles better.

Exercise 1

Measure the following angles:

,

Try finding the measurement using a protractor!

Exercise 2

Find the complementary angle of 35 degrees.

Complementary Angle = 90° - 35°

Calculate this, and you will get the complementary angle.

Exercise 3

Identify the supplementary angle of 135 degrees.

Supplementary Angle = 180° - 135°

Work out this calculation to find the answer.

Conclusion

Angles are all around us. They are important in a variety of fields, from construction to navigation. By understanding angles and their types, measuring them using a protractor, and knowing their relationships, we can solve many problems in geometry and see their appearance in our daily lives. Keep practicing, and soon measuring angles will become second nature!


Grade 5 → 6.2


U
username
0%
completed in Grade 5

← Prev (6.1)
Types of Lines and Angles
Next (6.3) →
Classifying Triangles

Comments 



Measuring Angles

https://www.buddymath.com/g5/6.2?bmal=en