3-2 Reading To Learn Mathematics Angles And Parallel Lines Answers

Angles

Angles are formed when two lines intersect at a point. The measure of the "opening" between these two lines is called an "Angle". It is denoted by using the symbol ∠. Angles are usually measured in degrees and radians, which is a measure of circularity or rotation. Angles are a part of our day-to-day life. Engineers and architects use angles for the design of roads, buildings, and sporting facilities. In the above image, we can see a surveyor using a Theodolite at a construction site to measure the angle. Let's see, how many of you like sports! Have you ever watched a game of football? Did you observe where the players take the corner kick from? Well, the point at which the lines intersect is what forms an angle!

1.	Parts of an Angle
2.	Types of Angles and Their Properties
3.	Angles Based on Rotation
4.	How to Measure an Angle?
5.	How to Construct Angles?
6.	FAQs on Angles

Parts of an Angle

In-plane geometry, an angle is formed when two rays are joined at their endpoints. There are different parts of the angle-

1. Two rays, which are called the sides of the angle. Look at the given image, sides OA and OB are sides of the angle AOB.

Sides of an Angle

2. The vertex of the angle, which has a common endpoint that is shared by the two rays. Observe the given image below with two rays as ray 1 and ray 2 with one green dot named as a vertex.

Vertex of an Angle

3. An angle is measured in degrees. One full rotation is equal to 360 degrees.

4. Size of an Angle: The best way to measure the size of an angle is to use a protractor. The standard size of a protractor is 180°. There are two sets of numbers on a protractor:

one in a clockwise direction
another in an anti-clockwise direction

A protractor is used to measure the size of an angle

Types of Angles and Their Properties

There are six types of angles. Each type of angle has a unique identification on the basis of angle measurement. Let us read about each type of angle individually along with their properties.

Acute Angle

An acute angle is an angle whose measure is greater than 0° and less than 90°.

Right Angle

When a measurement of an angle is equal to 90degrees it is known as a right angle. The right angle can be easily observed as it forms the shape of the letter L.

Obtuse Angle

When a measurement of an angle is less than 180 degrees but greater than 90 degrees it is an obtuse angle.

Straight Angle

The angle formed by a straight line is called a straight angle. It is one-half of the whole turn of a circle. The measure of the straight angle is 180°.

Reflex Angle

A reflex angle is an angle whose measure is greater than 180° but less than 360°

Complete Angle

When a measurement of an angle is equal to 360 degrees it is a complete angle.

Types of Angles

Angle Based on Rotation

Based on the direction of measurement or the direction of rotation, angles can be of two types:

Positive Angles
Negative Angles

Positive Angles
An angle measured by the counterclockwise (anti-clockwise) direction is a positive angle. From the origin, if an angle is drawn in the (+x,+y) plane, it forms a positive angle.

Negative Angles
Negative angles are those angles that are measured in a clockwise direction from the base. From the origin, if an angle is drawn towards the (−x,−y) plane, it forms a negative angle.

How to Measure an Angle?

We use protractors to measure angles. See the image given below. We can see ∠AOB. Let's try and see if we can find out what type of angle is ∠ AOB. Doesn't it look like an acute angle? This means that its measure is greater than 0° and less than 90°. Let us learn how to measure an angle using a geometrical instrument protractor.

Measuring angle AOB

Steps to measure ∠AOB.

Step1: Align the protractor with the ray OB as shown below. Start reading from the 0° mark on the bottom-right of the protractor.

Protractor showing how to measure angle

Step 2: The number on the protractor that coincides with the second ray is the measure of the angle. Measure the angle using the number on the "lower arc" of the protractor. Thus, ∠ AOB = 37°

Measuring angle using protractor

Next, let us try to measure this ∠AOC.

measure a given angle

Step 1: Measure the angle from the 0° mark on the bottom-left.

Measure the angle from the 0 degree

Step 2: The number on the "top arc" of the protractor that coincides with OA is the measure of ∠ AOC. Thus, ∠ AOC = 143°

measure angle AOC

How to Construct Angles?

We use a protractor to construct angles. Let's draw a 50° angle.

Step 1: First, draw a ray OB and align the protractor with OB as shown.

Constructing an angle using protractor.

Step 2: Place a point above the marking on the protractor that corresponds to 50°.

Measuring angle

Step 3: Remove the protractor and draw a ray beginning at O that passes through this point. Thus, ∠AOB is the required angle, that is ∠ AOB = 50°

angle between two rays

Note: If the ray extends in the other direction, we measure the angle from the 0° mark on the bottom-left.

The image given below shows how to draw a 50° angle when the ray is pointing in another direction.

measure the angle

Angle pointing at left hand side direction

Important Notes on Angles

0°< Acute angle < 90°
90°< Obtuse angle < 180°
180° < Reflex angle < 360°
Right angle equals to 90°
Straight angle equals to 180°.
Protractors usually have two sets of numbers going in opposite directions. When in doubt, think "Should this angle be bigger or smaller than 90°?"

☛ Related articles on Angles

Given below is the list of topics that are closely connected to angles. These topics will also give you a glimpse of how such concepts are covered in Cuemath.

Pairs of Angles
Transversals and Related Angles
Corresponding Angles
Interior Angles
Protractor
Supplementary Angles
Complementary Angles

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FAQs on Angles

What is an Angle in Math?

In-plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is denoted using the symbol ∠.

What are the 6 Types of Angles?

The 6 types of angles are right angles, acute angles, obtuse angles, straight angles, reflex angles, and complete angles.

How do you Describe Angles?

In-plane geometry, an angle can be described as a figure formed by two rays meeting at a common endpoint called the vertex of the angle.

☛ Also Check:

Angles Worksheets
Angles in Quadrilateral Worksheets
Geometry Angles Worksheets

What are the Types of Angles Based on Rotation?

Based on the direction of measurement or the direction of rotation, angles are of two types:

Positive Angles
Negative Angles

What is the Difference Between a Straight Angle and a Reflex Angle?

The angle formed by a straight line is called a straight angle. The measure of the straight angle is 180°. Whereas, a reflex angle measure is greater than 180° but less than 360°.

What are the Types of Angles Formed When a Transversal Passes Through Parallel Lines?

When a transversal passes through parallel lines, many pairs of angles are formed, such as corresponding angles, vertically opposite angles, alternate interior angles, and alternate exterior angles. All these pairs of angles are equal in measure.

What are the Types of Angles that Measure Less than 180°?

There are two types of angles that measure less than 180°, i.e., acute and obtuse angles. The measure of acute angles is always less than 90° while obtuse angles are more than 90° but always less than 180°. Examples of an acute angle are 50°, 60° and examples of obtuse angles are 170°, 165°.

What Is the Sum of all the Three Angles of Triangle?

The sum of the three angles of a triangle is 180 degrees.

☛ Check now:

Angles of a Triangle Worksheets
Triangle Angles Calculator

How Many 90 Degrees Angles Are There in a Straight Angle?

There are two 90 degrees angles in a 180-degree angle or straight angle. As the sum of two 90 degree angles is equal to 180 degrees, also the half of 180 degrees is 90 degrees. Thus twice 90-degree angles are there in a straight angle.

List the Types of Angles in Pairs?

The types of angles in pairs are listed below:

Adjacent angles
Complementary angles
Supplementary angles
Alternate interior angles
Alternate exterior angles
Corresponding angles
Vertical angles
Co-interior angles

What is a Complete Angle?

When an angle completes its full rotation starting from 0 degrees and ends at 360 degrees it is known as a complete angle, Its measurement is equal to 360 degrees.