How To Draw 180 Degree Angle

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Angles are measured in degrees (or radians), and there are many types of angles in geometry; acute, obtuse, right angle, half a circle, full rotation, etc. A full circle is 360 degrees, and all angles lie within that. 


An angle that measures exactly 180 degrees is called a straight angle. Another 180-degree angle name is half a circle. If a straight line is split into two and we know one angle, we can always calculate the other since a straight line is always 180 degrees, so the sum of the angles would be 180 degrees. 


In radians, a 180-degree angle is represented as π (pi). 


You can find a 180-degree angle picture below:

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In this article, we will see the details of 180 angles and how to draw 180-degree angles.


Types of Angles

Let us take a quick at all possible types of angles that can exist within a circle and their measurements. 

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  • Acute Angle  

Any angle that is more than 0 degrees and less than 90 degrees is an acute angle.

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  • Right Angle  

Right angle is 90 degrees exactly.

  • Obtuse Angle 

Any angle that is more than 90 degrees and less than 180 degrees is an obtuse angle.

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  • Straight Angle  

Straight angle is 180 degrees exactly.

  • Reflex Angle 

An angle that is more than 180 degrees and less than a full revolution or 360 degrees is a reflex angle. 

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  • Full Rotation  

Full rotation is 360 degrees exactly.

You can easily find all the angles in one place in the diagram below:

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Steps of Construction of 180 Degree Angle

To construct any angle we would need two things:

  • Compass

  • Ruler

Before we tell you how to draw a 180-degree angle, let us familiarize ourselves with the basics of a compass.

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A compass is a tool that helps in finding directions. It has a magnetic needle that always points at the magnetic north. One can find the direction by the angle that the desired object direction and the magnetic needle make.

We will now look into the steps of construction of 180-degree angle:

  • Draw a straight line l, using a ruler

  • Mark a point “O” anywhere on the line l.

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  • Keeping O as the centre, use a compass to draw arcs of any radius (from the left of O to the right of point O) which should cut the line. Let the points at which it cuts the line be A and B.

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  • The angle BOA is the straight angle or 180 degrees.

  • You can verify if it is a 180 angle or not, by using a protractor. Keep the protractor at the top of the point O and then measure the angle BOA. It should show as 180 degrees.

Examples of Straight Angle

You notice many straight lines in your day to day lives, some common examples are:

  • A flat surface - This has an angle of 180 degrees.

  • A see-saw is a straight angle example.

  • A stick is 180 degrees at the centre.

Straight line and straight angle are not the same. The straight angle measures 180 degrees and a straight line connects the two points.


Straight Angle Theorem

As per the straight angle theorem, all straight angles represent 180 degrees. In an angle, if its legs are pointing in exactly opposite directions, it forms a straight or 180 angle. The line segment in geometry is a good example of a straight angle as its endpoints extend in opposite directions.

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Straight Angle Properties

We have listed here a few key properties of a straight angle:

  • A straight angle is a measure of half of a revolution.

  • We can produce a straight angle by revolving one ray of a line segment by exactly 180 degrees with respect to the other ray.

  • The arms of a straight angle extend in opposite directions.

  • A straight angle modifies the direction of a point.

  • You can get a straight angle by joining two right angles.

Positive and Negative Angles

Starting from a line, there are two ways you can measure the angle: clockwise and anticlockwise. 

  • Positive Angle 

The direction of a positive angle is counterclockwise i.e. opposite to the direction in which a clock goes.

  • Negative Angle 

This is measured clockwise.

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When you are measuring and naming an angle to be sure of which angle you have been asked for and measure it counter-clockwise (positive angle)

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In the figure above, the smaller angle is obtuse while the bigger one is a reflex angle.

FAQ (Frequently Asked Questions)

Q1: Explain the Different Parts of a Compass.

Ans: To draw any angle, it is important to know parts of a compass. 

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The parts of a compass that we must understand for drawing any angle are:

  • Base plate - It is the rectangular bottom of the compass plate. It holds the compass housing and helps translate data from maps into useful real-world information (for example, how we get to the river, it will show the direction). 

  • Scales and rulers - Some lines and numbers are running along the edges of the baseplate. They tell you about the distances on paper and how to convert them into actual distances (inches to miles etc.). 

  • The direction of travel arrow - It is on the base plate and in a short triangle shape. If you hold the compass flat on your palm, the arrow will point forward in a direction that is away from you. This is useful during navigations, and hikers use it a lot.

  • Magnifier - This helps users to take a closer look at the tiny details of the map. 

  • Index line - This sits on the opposite end of the magnifier, which is the endpoint of the straight line from the direction of the travel arrow touching the dial.

  • Dial - This is a circle rotating around the housing and has degrees marked from 0 to 360 degrees.

Q2: What is Meant By Related Angles and How Many Types are There?

Ans: There are pairs of angles defined that make up a related angle. These are related to each other through a certain condition. Each of these pairs has been given a specific name and there are four common ones:

  • Supplementary angles - Two angles that sum up to 180 degrees are called together supplementary angles. For example, 120 degrees and 60 degrees are supplementary angles as their sum is 180 degrees.

  • Complementary angles - Two angles that sum up to 90 degrees are called together complementary angles. For example, 60 degrees and 30 degrees are complementary angles as their sum is 90 degrees.

  • Adjacent angles - In a plane, two angles are said to be adjacent if they satisfy all the below-mentioned conditions:

  1. They have a common arm 

  2. They have a common vertex

  3. Their non-common arms lie on the opposite sides of the common arm.

In the figure below, ∠AOC and ∠BOC are adjacent angles. Here OC is the

common arm and AO and OB are the two non-common arms on either side of OC.

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  • Linear pair - If two adjacent angles give a sum of 180 degrees, then they are termed as a linear pair. In a linear pair, the non-common arms are two opposite rays.

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In the image above, ∠AOC and ∠BOC form a linear pair.