Angles

● Identify an angle

● Identify a right angle 

● Identify an acute angle, an obtuse angle, a straight angle and a

reflex angle, in terms of the right angle.

                                                                                                                       

Angles

Angles are formed when two lines intersect at a point. The measure of the 'opening' between these two rays is called an 'angle'. It is represented by the symbol ∠. Angles are usually measured in degrees and radians, which is a measure of circularity or rotation. Engineers and architects use angles for the design of roads, buildings, and sporting facilities. Let us learn more about the definition of angles in Math's, the meaning of angles, the different properties of angles along with some angle examples.

What are Angles?

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.

Identifying an Angle

                                            Identifying An Angle

As seen in the illustration, an angle is created when two segments of a straight line intersect. Where the two segments of a straight-line meet are referred to as the angle's vertex.

The two straight line segments are known as the arms of the angle. The angle is marked.
with a curved line segment as indicated in red.

Identifying different types of angles in terms of the right angle

 Identifying different types of angles in terms of the right angle

                                                                                                                                                                            1.Acute Angle        

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to 90 degrees). For example, ∠30o, ∠45o, ∠60o, ∠75o, ∠33o, ∠55o, ∠85o, etc. are all acute angles. Let us see some examples here to understand.

2. Straight Angles

In geometry, a straight angle is an angle, whose vertex point has a value of 180 degrees. Basically, it forms a straight line, whose sides lie in opposite directions from the vertex. It is also termed as “flat angles.”

3. Obtuse Angles

Obtuse Angle Definition in Mathematics, “an obtuse angle is an angle which is greater than 90 ° and less than 180 °”. In other words, an obtuse angle is between a right angle and a straight angle.

4. Reflex Angles

As per the definition of reflex angle, any degree which lies between a straight angle (180°) and full rotation (360°) is a reflex angle. Hence, 181°, 190°, 200°, 210°, 220°, 230°, 240°, 250°, 260°, 270°, 280°, 290°, 300°, 310°, 320°, 330°, 340°, 350°, 359°, are all reflex angles.

5. Right Angle

When an angle measures 90°, it is known as a right angle. A right angle can be easily observed as it forms the shape of the letter L.

How to measure angle?

 

How to Measure an Angle?

We use protractors to measure angles. Observe the figure given below which shows ∠AOB. Let us 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 this angle using the protractor.

                                                                                                                                                                         

Important Notes on Angles

• 0°< Acute angle < 90°
• 90°< Obtuse angle < 180°
• 180° < Reflex angle < 360°
• A right angle is equal to 90°
• A straight angle is equal to 180°.

Examples

 Example 1: Observe the measure of the angles and identify the type of angles for each figure.

Solution:

a) The given angle is equal to 40°. It is an acute angle because its measure is less than 90°.

b) The given angle is equal to 117°. It is an obtuse angle because its measure is greater than 90° but less than 180°.

c) The given angle is equal to 121°. It is an obtuse angle because its measure is greater than 90° but less than 180°.

d) The given angle is equal to 185°. It is a reflex angle because its measure is greater than 180° but less than 360°.

Example 2: Classify the following angles into acute angles, obtuse angles, right angles, or reflex angles.

a) 24°

b) 150°

c) 90°

d) 270°

Solution:

(a) 24° lies in between 0° and 90°, so it is an acute angle.

(b) 154° lies in between 90° and 180°, so it is an obtuse angle.

(c) 90° is known as the right angle.

(d) 270° lies in between 180° and 360°, so it is a reflex angle.

Example 3: Write true or false for the following statements:

a.) 180° < Reflex angle < 360°

b.) 0°< Obtuse angle < 90°

c.) The two rays which join at a common point to form an angle are called the arms of the angle.

Solution:

a.) True, 180° < Reflex angle < 360°

b.) False, 0°< Acute angle < 90°

c.) True, the two rays which join at a common point to form an angle are called the arms of the angle.

Videos

 

 Acknowledgement 

Most of the information in this session have been taken from internet and textbook with thanks.

S.Sudharshan.