180 Degree 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 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 a degree. It is denoted by the symbol °.

Types of Angles

There are different types of angles. They are:

• 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 a 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 their sum is 180°.

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

Table of Angles

Here is a description of each angle, as stated by the definition of different angles mentioned in geometry. Suppose θ is any angle, then;

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 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 angles in our day-to-day life are:

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

• A straight stick has an angle that is straight or equal to 180 degrees.

• A plane inclined staircase represents a straight angle.

• The clock showing 6 o'clock forms a straight angle.

• Angle formed in a see-saw.

Note: A straight angle is different from a straight line, as a straight angle measure 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 a straight line is the line segment in geometry, the endpoints of which extend 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 to another ray.

• At 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 Protractor

Follow are the steps that will help to construct a 180-degree angle with the help of a protractor:

• Draw a ray OB.

• Then place the protractor at point O.

• In the inner circle of the protractor, search for 180° reading and mark a dot with a pencil, and name it C.

• Join the points O and C. 

• Now, ∠BOC=180-degree angle.

How to Draw 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 centre, 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 Examples

A. 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 be 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°.

B. Find the angles if two angles are equal to one other and also supplementary.

Solution: Two angles are equivalent in this case. Let the angles be denoted as ‘x’.

Furthermore, because the two angles are supplementary,

x + x = 180°

2x = 180°

x = 180/2

x = 90°

Therefore, both angles are 90° each.

C. Angles A, B, and C form a straight angle together. Find the measurement of angle C if angle A is 30° and angle B is 90°.

Ans: We all know that a straight angle is a 180° angle. 

That means, angle A + angle B + angle C = 180 degrees.

30° + 90° + C = 180°

C = 180° - 90° - 30° = 60°

Hence, the measurement of angle C is 60°.

We hope that this article on the 180-Degree angle helped you. Understand the concept of drawing an angle and what 180-degree angle stands for. Follow the solved examples to understand how the concept is being used.