Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Geometry → Lines and Angles ↓


Types of Angles


In the study of geometry, understanding angles is a fundamental concept. Angles are formed when two lines or rays diverge from a common point called the vertex. Angles help us understand and describe how two lines relate to each other. They are also used in a variety of applications such as construction, engineering, art, and more. In this comprehensive guide, we will explore the different types of angles and how they fit into the realm of geometry.

Basic definitions of angles

An angle is formed where two lines or rays meet. The point where they meet is called the vertex. The two lines or rays are called the sides or arms of the angle. The most common description of an angle includes the common point, the vertex, and the degree of rotation from one side to the other.

The size of an angle is measured in degrees, using a protractor. A full circle has 360 degrees. Angles can also be measured in radians, but for the purposes of most basic geometry, we'll focus on degrees.

Types of angles based on their measure

1. Acute angle

An acute angle is an angle whose measure is less than 90 degrees. It is the smallest angle that can be formed without being a zero-degree angle (a line). Here's a simple example:

θ

In this image, the angle θ formed by the two lines is less than 90 degrees, making it an acute angle. Examples of acute angles include 30°, 45°, and 60°.

2. Right angle

A right angle is exactly 90 degrees. A right angle is one-quarter of a full rotation around a point. Right angles are often found in elements of our everyday life, such as the corners of books, tables, and rooms. A right angle looks like this:

90°

Here the lines come together to form an L-shape, which is characteristic of a right angle. Recognizing right angles is important in ensuring that structures are aligned correctly.

3. Obtuse angle

An obtuse angle is an angle that is more than 90 degrees but less than 180 degrees. These angles appear more open or wider than right angles. Here's an example:

θ

The angle θ extends beyond 90°, but is still not a straight line, which confirms it as an obtuse angle. Examples include angles such as 120°, 135°, and 145°.

4. Straight angle

A straight angle is exactly 180 degrees. It appears as a straight line, hence the name. It looks like this:

180°

Since a straight angle is formed where two opposite directions meet, it actually forms half of a full circle. Understanding this type of angle is important for understanding symmetry and direction.

5. Reflex angle

A reflex angle is any angle greater than 180 degrees but less than 360 degrees. Reflex angles appear as large, open angles and are usually represented by the side opposite the smaller angle. Here's an example:

θ

In this diagram, the angle around the point θ that is greater than 180 degrees is a reflex angle. Examples of reflex angles are 210°, 250°, and 315°.

Special cases and other types of angles

Zero angle

A zero angle is an angle of exactly 0 degrees. This occurs when the two sides of the angle overlap each other completely. Here's an illustration:

Although it is not often discussed, the zero angle is theoretically accepted in geometry.

Full rotation (or full angle)

A complete rotation or full angle is one that measures exactly 360 degrees. This is an important concept because it represents a complete, one-time rotation around a central point. A complete angle visually encompasses a whole circle.

Supplementary angles

Two angles are complementary if the sum of their measures is 90 degrees. The angles do not need to be adjacent, meaning they do not need to be next to each other or part of the same diagram. For example, if angle A measures 30 degrees and angle B measures 60 degrees, then angle A and angle B are complementary.

Obtuse angle

Conversely, two angles are complementary if the sum of their measures is 180 degrees. These angles can be adjacent or nonadjacent. For example, if angle C measures 110 degrees and angle D measures 70 degrees, then angle C and angle D are complementary.

Here is a visualization of complementary and supplementary angles:

Supplement Supplement

Conclusion

Understanding angles and the difference between different types of angles is fundamental to delving deeper into the world of geometry. Angles not only inform our understanding of shapes and spaces but also enhance our abilities in areas dependent on precision and design.

From acute to reflexive and zero to complete rotation, each type of angle has its own significance and application. Complementary and supplementary angles further enrich our knowledge, showing how angles interact with each other. Knowing how to identify and work with angles will strengthen your mathematical knowledge and enhance your problem-solving skills.

Keep practicing drawing and identifying these angles with real-world objects, and you'll find your understanding of geometry becomes stronger and more intuitive.


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Types of Angles

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