Why Learning to Draw 180° Angles Matters in Geometry
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.
FAQs on How To Draw a 180 Degree Angle: Step-by-Step Instructions
1. How do you draw a 180-degree angle using a protractor step-by-step?
Drawing a 180-degree angle, also known as a straight angle, is a simple process using a protractor. Follow these steps:
Step 1: Draw a straight horizontal line on your paper using a ruler. This line is one of the arms of your angle. Label one end of the line as point O (the vertex) and the other as point A.
Step 2: Place the centre point of your protractor on the vertex O. Align the baseline of the protractor with the arm OA you just drew.
Step 3: Look for the 180° mark on the protractor's scale. Mark a dot at this point and label it B.
Step 4: Remove the protractor and draw a line connecting the vertex O to the point B. You will notice that the line OB extends in the exact opposite direction to OA, forming a single straight line.
The resulting figure, ∠AOB, is a perfect 180-degree angle.
2. What is a 180-degree angle called, and what does it look like?
A 180-degree angle is called a straight angle. As the name suggests, it looks exactly like a straight line. It is formed when two rays, starting from a common vertex, point in directly opposite directions. For example, the hands of a clock at 6:00 PM form a straight angle.
3. Can a triangle have a 180-degree angle inside it? Explain why or why not.
No, a triangle cannot have a 180-degree angle as one of its interior angles. This is a common point of confusion. While the sum of the three interior angles of any triangle is always 180 degrees, a single angle cannot be 180 degrees. If one angle were 180 degrees, the two sides forming that angle would create a straight line, making it impossible to form a closed three-sided figure, which is the definition of a triangle.
4. What is the importance of the 180-degree angle concept in geometry?
The 180-degree angle is a fundamental concept in geometry for several reasons:
Foundation for Lines: It defines what a straight line is in terms of angles.
Supplementary Angles: It is the basis for supplementary angles, where two angles add up to 180 degrees. This property is crucial for solving problems involving intersecting lines.
Triangle Angle Sum Theorem: It establishes the rule that the interior angles of a triangle sum to 180 degrees.
Polygons: It is used in formulas to calculate the sum of interior angles in polygons, such as quadrilaterals, pentagons, and more.
5. What is the main difference between a 180-degree angle and a 360-degree angle?
The main difference lies in their formation and appearance. A 180-degree angle (straight angle) is half of a full rotation and looks like a straight line. A 360-degree angle (complete angle) represents a full rotation, where the starting and ending arms of the angle are in the exact same position, completing a full circle.
6. How are supplementary angles related to a 180-degree angle?
Supplementary angles are directly defined by the 180-degree angle. Two angles are said to be supplementary if their sum is exactly 180 degrees. When two supplementary angles are placed adjacent to each other (sharing a common vertex and arm), their non-common arms form a straight line, which is a 180-degree angle. This pair of adjacent supplementary angles is also known as a linear pair.
7. Can you construct a 180-degree angle with a compass? If so, how is it different from using a protractor?
Yes, you can construct a 180-degree angle with a compass and a ruler. The simplest method is to just draw a straight line with a ruler, which is inherently a 180-degree angle. Alternatively, you can construct a 60-degree angle and then extend it twice to make 180 degrees. The key difference is in the process:
Using a protractor involves measuring a pre-defined angle.
Using a compass involves constructing the angle from basic geometric principles without pre-set measurements.
For simply drawing an angle, a protractor is more direct. For pure geometric construction, a compass is used.
