What is a 180 Degree Angle Called?
The concept of 180 degree angle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.
What Is 180 Degree Angle?
A 180 degree angle is called a straight angle in geometry. This angle forms a straight line, and its measurement is exactly 180°. You’ll find this concept applied in areas such as triangles (angle sum property), supplementary angles, and the study of various types of angles in geometry.
Definition and Angle Types
An angle is formed when two rays meet at a common point called the vertex. When the arms of an angle point in exactly opposite directions, they form a straight angle. Here’s how the 180° angle fits among other angle types:
| Angle Type | Measure | Shape/Example |
|---|---|---|
| Acute angle | 0° < θ < 90° | Sharp corner (like a pizza slice) |
| Right angle | θ = 90° | Corner of a square |
| Obtuse angle | 90° < θ < 180° | Door open wide but not flat |
| Straight angle (180 degree angle) | θ = 180° | Flat, straight line |
| Reflex angle | 180° < θ < 360° | Bent back past flat |
| Full rotation | θ = 360° | Full circle (clock) |
Visual Examples of 180 Degree Angle
A 180 degree angle looks like a completely flat angle, forming a straight line. Here are real-life and geometric examples:
- Opened book lying flat on a table (spine forms the angle)
- Clock hands at 6 o’clock (minute and hour hands in straight line)
- A ruler or stick placed flat
- Straight edge of a protractor measuring 180°
Properties of 180 Degree (Straight) Angle
- The arms (rays) point in exactly opposite directions.
- Measures exactly 180°.
- Divides a circle into two equal halves (semi-circle).
- Is formed by a single straight line.
- Supplementary angles add up to 180°.
- The sum of the three angles in every triangle is 180°.
Key Formula for 180 Degree Angle
Here’s the standard formula: \( \text{Straight angle} = 180^\circ \)
- Supplementary Angles: \( \angle A + \angle B = 180^\circ \)
- Triangle Angle Sum: \( \angle A + \angle B + \angle C = 180^\circ \)
How to Draw a 180 Degree Angle
- Draw a straight line (this will be the base or one arm).
- Mark a point as the vertex anywhere on this line.
- Place the center of the protractor on the vertex, align the baseline with the straight line.
- Find 180° on the scale and mark a dot at this position.
- Draw a second ray from the vertex through this dot—the angle between the two rays is 180°.
Solved Example: Supplementary Angles
Suppose a straight angle is divided into two parts, with one angle measuring 70°. What is the measure of the other angle?
1. Let the unknown angle be \( x \).
2. Given, other angle = 70°.
3. By the straight angle property: \( x + 70 = 180 \)
4. So, \( x = 180 - 70 = 110° \)
Final answer: The other angle is 110°.
Comparison: 180 Degree Angle vs Other Angle Types
| Angle | Measure | Name | Shape |
|---|---|---|---|
| Angle between arms at 90° | 90° | Right angle | L-shape/corner |
| Angle between arms at 180° | 180° | Straight angle | Flat/straight line |
| Angle between arms at 360° | 360° | Full/Complete angle | Circle |
Application in Triangles and Mathematics
The 180 degree angle is essential for understanding the angle sum property of triangles—every triangle’s angles add up to 180°. In trigonometry, knowing that a straight line represents 180° helps in graphs and solving equations. Supplementary angles, commonly asked in exams, also directly relate to this angle. If you want more detail, check our page on Angle Definition or review Straight Angle for extended examples.
Frequent Errors and Misunderstandings
- Confusing a 180° angle (straight) with a 360° angle (circle or full rotation).
- Thinking a straight line is not an angle—it actually is a straight angle.
- Believing two obtuse angles can add up to 180° (only if they are perfectly supplementary).
- Mixing up supplement and complement (complementary is 90°, supplementary is 180°).
Relation to Other Concepts
The idea of a 180 degree angle connects closely with supplementary angles, types of angles in geometry, and reflex angle (which is any angle greater than 180° but less than 360°). Mastering this helps in learning geometric proofs, polygon properties, and more advanced trigonometric identities.
Classroom Tip
A quick way to remember a 180 degree angle is to visualize the hands of a clock at 6 o’clock or simply see any flat, straight line. Vedantu’s teachers often use this tip during live classes and suggest practicing by opening a book flat on your desk to see the straight angle in real life.
Try These Yourself
- Name three objects at home that form a 180 degree angle when placed straight.
- If angle A is 110°, what is its supplement?
- Draw a straight angle using a protractor and label its arms.
- What happens if you add two right angles together?
We explored 180 degree angle—from definition, properties, construction steps, applications, examples, and how it relates to other geometry concepts. Continue practicing with Vedantu and explore related topics like Types of Angles, Straight Angle, and 360 Degree Angle to become confident in working with all types of angles.
FAQs on 180 Degree Angle Explained with Examples
1. What is a 180-degree angle called in geometry?
A 180-degree angle is formally called a straight angle. It is also sometimes referred to as a flat angle because its two rays point in opposite directions, forming a perfectly straight line.
2. What are the main properties of a 180-degree angle?
The main properties of a 180-degree angle, or a straight angle, are:
It measures exactly 180 degrees (or π radians).
It appears as a perfectly straight line.
It represents half of a full rotation (which is 360 degrees).
Any two adjacent angles that form a straight angle are called supplementary angles.
3. Can you give some real-life examples of a 180-degree angle?
Yes, a 180-degree angle is common in everyday life. Some examples include:
The hands of a clock at exactly 6:00.
A straight road or a ruler's edge.
A book opened completely flat on a table.
The surface of a calm sea at the horizon.
4. How is a 180-degree angle different from a straight line?
While a 180-degree angle forms a straight line, they are different concepts. A straight line is a one-dimensional figure that extends infinitely in both directions. A 180-degree angle is a specific *measurement* of rotation between two rays originating from a common vertex. The angle is the measure of the turn, while the line is the geometric shape.
5. What is the correct way to draw a 180-degree angle?
To draw a 180-degree angle, simply use a ruler to draw a straight line. Then, place a point (the vertex) anywhere on that line. The two rays extending from the vertex in opposite directions form a straight angle of 180 degrees. You can confirm the measurement using a protractor by placing its center on the vertex.
6. Why is the 180-degree angle a fundamental concept in geometry?
The 180-degree angle is fundamental because it forms the basis for the linear pair axiom, which states that angles on a straight line add up to 180°. This principle is essential for proving many other geometric theorems, including the fact that the sum of interior angles in any triangle is always 180°.
7. How does a 180-degree angle relate to supplementary angles?
The relationship is direct and definitional. Two angles are called supplementary if their measures add up to 180 degrees. Therefore, when you place two supplementary angles adjacent to each other, they will always form a single straight angle.
8. Can an interior angle inside a polygon be 180 degrees?
No, a simple polygon like a triangle or a quadrilateral cannot have an interior angle of exactly 180 degrees. If an angle were 180°, the two sides forming that vertex would simply create a straight line segment, and the shape would not be a closed polygon with a distinct corner at that vertex.
9. What is the difference between making a 180-degree turn and a 360-degree turn?
A 180-degree turn means reversing your direction to face the exact opposite way. In contrast, a 360-degree turn (a complete angle) means performing a full rotation and ending up facing the same direction you started in.
10. Does a 180-degree angle have a specific formula?
A 180-degree angle does not have a formula; it is a constant value representing a specific amount of rotation. However, it is a key component in other formulas, such as the formula for finding a supplementary angle (180° - given angle) or the formula for the sum of interior angles of a polygon, which is (n-2) × 180°, where 'n' is the number of sides.
