180 Degree Angle

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What is an Angle?

An angle can be defined as the combination of two rays with a common endpoint. The symbol for an angle is ∠. The corner point of an angle is basically known as the vertex of an angle. The two straight sides of the angle are known as the arms of the angle.


The angles which are measured anticlockwise from the base are something we call positive angles. The angles measured clockwise from the base are called negative angles. The standard unit of measuring an angle is known as degree. It is denoted by the symbol °.


Types of Angles

  • Reflex Angle: A reflex angle can be defined as an angle that measures more than 180° but less than 360°.

  • Straight Angle: The straight angle can be defined as an angle whose measure is 180 degrees. Its straight angle looks like a straight line. They are collinear and opposite rays. When we keep a thin book open, we can see that the angle formed between the two pages is an example of the straight angle.

  • Adjacent Angle: Two angles are known to be adjacent when they share a common side and a vertex.

  • Vertically Opposite Angles: Vertically opposite angles are basically angles that are formed opposite to each other when two lines intersect.

  • Complementary Angles: Two angles are known to be complementary when the two angles add up to 90°.

  • Supplementary Angles: Two angles are known to be supplementary when adding up to 180°.

As per the definition of the different angles present in geometry, here is a brief description for each angle. Suppose we have any angle namely θ , then;


Table of Angles

Acute angle

0° < θ < 90°

Right angle

θ = 90°

Obtuse angle

90° < θ < 180°

Straight angle

θ = 180°

Reflex angle

180° < θ < 360°

Full rotation

θ = 360°


180 Degree Angle

A straight angle is an angle that changes the direction to point the opposite way. It looks like a straight line. A straight angle measures 180° (that is equal to half a revolution, or π radians,or two right angles).


In radians, the 180-degree angle is measured in pi (that is π). To point the opposite way, the straight angle generally changes the direction. A 180 degree is also considered as supplementary. Apart from this angle, there are five different types of angles in geometry that you can learn here.


Notation

In degrees, the straight angle is represented as 180 degrees and in radians, it is denoted with pi (π).


Straight Angle Examples

Some of the examples of straight angle in our day-to-day life are:

  • A flat surface has an angle equal to 180 degrees.

  • A straight stick has an angle which is straight or equal to 180 degree.

  • A plane inclined staircase represents a straight angle.

  • Angle formed in a see-saw.

Note: A straight angle is different from a straight line, as a straight angle measures 180 degrees and a straight line is basically a connector of two points.


The Theorem of Straight Line

The straight angle theorem states that all the straight angles are 180 degrees. If the legs of the angle are pointing exactly in the opposite directions, then it forms a straight angle. A straight angle is represented as 180° (that is in degrees) or π (in radians).

One good example of straight line is the line segment in geometry, the endpoints of which extends towards the opposite direction.


What are the Properties of Straight Angles?

Some important properties of straight angles are as given below:

  • A straight angle basically measures exactly half of a revolution.

  • A straight angle is produced by revolving one ray by 180 degrees with respect to another ray.

  • In any straight angle, the arms extend in the opposite directions.

  • A straight angle generally modifies the direction of a point.

  • A straight angle can also be formed by joining any two right angles.

How to Draw a 180-Degree Angle With the Help of a Compass?

To draw the straight angle using a compass follow the below steps:

  • First, draw a straight line using a ruler or scale and name it XY.

  • Now mark a point O anywhere between X and Y.

  • With point O as the center, draw an arc of any radius using a compass, from the left of point O to the right of O.

  • This arc cuts the straight line at point P and point Q.

  • Hence, the angle POQ is the required 180 degrees.

Drawing Angles Less than 180° With a Protractor

To draw an angle using a protractor, proceed as follows:

  • First, you need to draw a straight line (i.e. an arm of the angle).

  • You need to place a dot at one end of the arm and this dot represents the vertex of the angle.

  • You need to place the baseline of the protractor along the arm of the angle and the centre of the protractor at the vertex dot. 

  • You need to find the required angle on the scale and then you need to mark a small dot at the edge of the protractor.

  • Join the small dot to the vertex with a ruler which will help to form the second arm of the angle.

  • Label the angle with capital letters.

Solved Example

If a straight angle is divided into two parts, and one angle measures 60 degrees, then find the other angle.


Solution) Let the unknown angle is x

Given, another angle = 60°

We know that;

Straight angle = 180°

Therefore,

x + 60 = 180

x = 180 - 60

x = 120°

Hence, the other angle measures equal to 120°.

FAQ (Frequently Asked Questions)

Question 1) What is the Angle of 180 Degrees?

Answer) A 90° angle is called a right angle. An angle between 90° and 180° is known as an obtuse angle. An angle that is less than 90° is known to be an acute angle. More about angles, degrees, and similar figures. Half a circle is equal to 180 degrees (a straight angle).

Question 2) What Does a 180-Degree Angle Look Like?

Answer) A straight line creates a 180-degree angle. It is always equal to one-half a rotation around a full circle. A straight line that is a 180 degree angle is equal to three-quarters of a rotation around a circle. A full circle creates a 360-degree angle.

Question 3) What are the 5 Types of Angles?

Answer) The types of Angles - Acute angle, Right angle, Obtuse angle, Straight angle and Reflex angle.

Question 4) What is an Angle Between 180 and 360 Called?

Answer) Angles that are 90 degrees (θ = 90°) are right angles. Angles that are 180 degrees (θ equal to 180°) are known as straight angles. Angles between 180 and 360 degrees (180°< θ < 360°) are known as reflex angles.