Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Geometry → Basic Geometric Shapes ↓


Types of Angles


Geometry is an essential part of mathematics that deals with shapes, measurements, and the properties of space. Angles are one of the fundamental components of geometry. They are formed when two rays meet at a common end point called the vertex. Understanding angles is important as they are present in various objects and activities in our daily lives.

In geometry, angles can be classified into several types based on their measure. Each type has its own distinct properties that are useful in identifying and solving geometric problems. Let's learn about the different types of angles and their properties.

What is the angle?

An angle is formed by two rays or line segments that share a common end point, known as the vertex. The amount of bend between the two rays is called the angle. Angles are measured in degrees (°) and radians, but for basic geometry, we'll focus on degrees.

Types of angles

Angles may be classified into the following types depending on their measure:

Acute angle

An acute angle is an angle that measures more than 0° and less than 90°. These angles are sharp and small. Here's what they usually look like:

<0° < = <90°
acute angle

Right angle

A right angle is an angle that measures exactly 90°. It represents one-quarter of a full rotation and is often found in basic geometric shapes like squares and rectangles. The symbol for a right angle is a small square drawn between two rays.

= 90°
Right Angle

Obtuse angle

An obtuse angle is one that measures more than 90° but less than 180°. These angles appear wider than right angles but do not reach the straight line.

> 90° & < 180°
obtuse angle

Straight angle

A straight angle is exactly 180°. It forms a straight line and represents a half turn. Straight angles are usually seen in linear arrangements.

= 180°
straight angle

Reflex angle

The reflex angle is greater than 180° but less than 360°. It represents more than a half turn and occurs in scenarios where two rays form a large opening.

> 180° & < 360°
reflex angle

Full angle

A full angle is 360° and represents a complete turn. It forms a complete circle and is rarely distinguished among simple geometric shapes.

= 360°
Full Angle

Examples and exercises

Let's put this knowledge into practice with examples. Identify the type of angles in the following scenarios:

Example 1: Triangle angles

A triangle has three angles. If one angle in a triangle is 45°, while the other is 55°, what type of angle is the third angle?

To find it, subtract the sum of the existing angles from 180° (the total sum of the triangle):

180° - (45° + 55°) = 80°

The third angle is 80°, which is an acute angle because it is less than 90°.

Example 2: Time on the clock

What type of angle is formed between the hands of a clock when it is 3:00?

At 3:00, the hour hand is at 3, and the minute hand is at 12, forming a right angle (90°).

Example 3: Shapes and angles

A rectangle has four angles. What types of angles are present in the figure?

All angles of a rectangle are right angles (90°).

Conclusion

Understanding the different types of angles is important for identifying and solving geometric problems. Angles help us describe the turns and rotations associated with lines and shapes and form the basis for understanding more complex geometric shapes.

Practicing with angles in different scenarios can help reinforce this understanding and apply it to everyday situations, beyond the classroom.


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Points, Lines, and Angles
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Types of Angles

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