What is an Angle?

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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 corner vertex. The two right sides of an angle are known as the arms of the angle.

Angles measured counterclockwise from the base are what we call positive angles. Angles measured clockwise from the base are called negative angles. The standard unit of angle measurement is known as the 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°.

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

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

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

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

• Supplementary Angles: Two angles are known to be supplementary when their sum is 180°.

Following the definition of different angles in geometry, here is a brief description of each angle. Suppose we have some angle, namely θ, then;

Table of angles

Here is a description of each angle as stated in the definition of various angles mentioned in geometry. Let θ be any angle, then;

180 degree angle

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

In radians, an angle of 180 degrees is measured in pi (that’s π). If pointed in the opposite direction, a right angle generally reverses direction. 180 degrees is also considered extra. In addition to this angle, there are five different types of angles in geometry that you can learn about here.

designation

In degrees, a right angle is represented by 180 degrees, and in radians, it is represented by pi (π).

Examples of right angles

Some examples of right angles in our daily life are:

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

• A straight stick has a straight or 180 degree angle.

• A ladder inclined to a plane is a right angle.

• A clock showing 6 o’clock forms a right angle.

• The angle formed in the sight.

Note: A right angle is different from a straight line because a right angle is 180 degrees and a straight line is basically a connection between two points.

The straight line theorem

The Right Angle Theorem states that all right angles are 180 degrees. If the legs of an angle point in exactly the opposite direction, then it forms a right angle. A right angle is represented as 180° (this is in degrees) or π (in radians).

One good example of a straight line is a line segment in geometry whose endpoints extend in opposite directions.

What are the properties of right angles?

Some important properties of right angles are given below:

• A right angle generally measures exactly half a revolution.

• A right angle is formed by rotating one ray to another ray by 180 degrees.

• At any right angle, the arms extend in opposite directions.

• A right angle generally changes the direction of a point.

• A right 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 the steps to help you construct a 180 degree angle with the help of a protractor:

• Draw the ray OB.

• Then place the protractor at point O.

• Find the 180° reading on the inner circle of the protractor and mark a point with a pencil and call it C.

• Connect the points O and C.

• Now, ∠BOC=180-degree angle.

How to draw a 180 degree angle with the help of a compass?

To draw a right angle using a compass, follow the steps below:

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

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

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

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

• Therefore, the angle POQ is required to be 180 degrees.

Drawing angles less than 180° with a protractor

To draw an angle using a protractor, do the following:

• First, you need to draw a straight line (that is, the arm of the corner).

• You need to place a point at one end of the arm and this point represents the apex of the corner.

• You should place the baseline of the protractor along the angle arm and the center of the protractor at the vertex.

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

• Connect the small point with the tip ruler to help form the other arm of the corner.

• Mark the corner with capital letters.

Solved examples

A. If a right angle is bisected and one angle is 60 degrees, then find the other angle.

Solution: Let the unknown angle be x

Given, other angle = 60°

We know that;

Right angle = 180°

therefore

x + 60 = 180

x = 180 – 60

x = 120°

Therefore, the other angle is equal to 120°.

b. Find the angles if two angles are congruent and also supplementary.

Solution: In this case two angles are equal. Let’s denote the angles as ‘x’.

Furthermore, since these two angles are supplementary,

x + x = 180°

2x = 180°

x = 180/2

x = 90°

Hence, both angles are 90° each.

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

Answer: We all know that a right angle is an angle of 180°.

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

30° + 90° + C = 180°

C = 180° – 90° – 30° = 60°

Hence, the measure of angle C is 60°.

We hope this article has helped you 180 degrees. Understand the concept of drawing an angle and what a 180 degree angle means. Follow the solved examples to understand how the concept is used.

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