Did you ever notice the two hands of a clock? The two hands together make different sets of lines from a common point. These sets of lines from a common point is called angle. The two hands form different angles every minute of the time. A clock forms an example of angles in real life. What are the other examples of angles in real life? Let’s study the various types of angles, say acute angle, in real life and their examples in detail.

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## Angles

Before studying angle, let us do one interesting thing. Take a piece of paper and drawn a dot anywhere on it. Name this dot O. This dot O is called point. From this point draw as many straight lines as you can. How many did you get?

Draw another dot and name it P. Join OP. What did you get? A line segment OP with endpoints O and P. A line segment is a part of a line. Do you know a line has no endpoints like line segment? A line has many line segments in it.

Have you ever thought why we say sun rays and not sun line? Is ray different from a line? Yes, it is. A ray has one fixed point. It cannot go in both the direction like that a line. For sun rays, the Sun is the fixed point and thus we say the light coming as sun rays.

Draw one more point other than O and P and call it R. Now join OR and OP. What will you find? Two lines and a common point O. This is an angle. Ask your friend to do this activity. Are the two angles same every time? Maybe it is not.

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## Terminologies in Angles

Two lines or line segments or rays with a common point form an angle. An angle is denoted by a symbol ∠. An angle is measured in an anti-clockwise manner with the help of a protector in degree.

- Vertex: The common starting point in an angle is a vertex.
- Arms: The two rays forming an angle from a fixed point are arms. They are also called the sides of the angle.

- Measuring Angle: Place the center of the protector at the fixed point, say O of the angle at one of the arm. The other arm shows the degree of the angle when measured from the initial arm in an anti-clockwise manner.

## Types of Angles

There are different types of angles formed by two lines or rays with one common starting point. Based on the degree of measurement, the angles are classified as:

### Zero Angle

An angle whose measure is 0° is zero angle. The initial and the final arms are at the same position. ∠AOB is zero angle.

### Acute Angle

An acute angle is the one that is greater than 0° and less than 90°.

### Right Angle

Any angle whose measure is equal to 90° is a right angle.

### Obtuse Angle

An angle is said to be an obtuse angle if it is greater than 90° but is less than 120°.

### Straight Angle

An angle whose measure is 180° is a straight angle. This angle got its name as it forms a straight line. ∠AOB is a straight angle.

### Reflex Angle

A reflex angle is the one that is greater than 180° and less than 360°.

### Complete Angle

If the measure of an angle is 360°, it is a complete angle. This angle is formed as the arm makes one completes turn and returns to its starting position.

## Other Type of Angles

Apart from the above-mentioned angles, there are other types of angles too.

- Adjacent Angles: Two angles are adjacent if both of them have one common arm and a common vertex. ∠AOB and ∠COB are the adjacent angles. Is there any other pair of adjacent angles? ∠AOC and ∠COB, and ∠AOB and ∠AOC are another sets of adjacent angles.

- Complementary Angles: Two angles are complementary to each other if the sum of both the adjacent angles is 90°.

- Supplementary Angles: When the sum of a pair of adjacent angles is 180°, the angles are supplementary angles.

- Vertically Opposite Angles: Suppose two straight lines AB and CD intersect each other at a point O. The pairs of the opposite angles are vertically opposite angles (V.O.A). The V.O.A. are equal in measurement. Here, ∠1 = ∠2 and ∠3 = ∠4.

## Angles in Real Life

In the beginning, we have talked about angles formed by the hands of a clock. Consider an example, the clock shows the time is 3 o’clock in the morning. What is the angle made by both hands of the clock? It is a right angle. In direction, we can find various angles. Where else can we find angles?

Cloth-hangers, scissors, arrowhead, partly opened-doors, pyramids, Set squares, an edge of a ruler, an edge of tables, cycle spokes, wheels etc are examples of angles in real life. Different alphabets also form the examples of angles. What is the angle in letter V? An acute angle. Even we make different angles in different postures while doing yoga and exercises.

## Solved Examples for You

**Question 1**: Name the angle when the time in a clock is 3: 40 pm? Is it Obtuse or Reflex or Acute Angle?

**Answer:** The angle is measured in an anti-clockwise manner and thus the angle formed is reflex and not obtuse or acute angle.

Problem: What is the value of angles α, β?

Solution: α = 90° + 45° = 135° and β = 180°.

**Question 2: What is an Angle?**

**Answer: **An angle is formed by two lines or line segments or rays with a common point. We make use of the symbol ∠ to denote an angle. We measure it in an anti-clockwise manner by using a protractor in a degree.

**Question 3: What are the different types of Angles?**

**Answer:** On the basis of the degree of measurement, we classify the angles as Zero Angle, Acute Angle, Right Angle, Obtuse Angle, Straight Angle, Reflex Angle and Complete Angle.

**Question 4: What are complementary and supplementary angles?**

**Answer**: Complementary angles are those when two angles are complementary to each other if the sum of both those adjacent angles is 90°. Similarly, supplementary is when the sum of a pair of adjacent angles equals 180°.

**Question 5: What is an acute angle example?**

**Answer:** An acute angle is one where the angle measures less than 90 degrees. A triangle that forms by all angles measuring less than 90 degrees is also an acute triangle. For instance, an equilateral triangle consists of all 3 angles measuring 60°, thus it makes it an acute triangle.