Straight Angle

Straight Angle Definition

When one arm is moved from the vertex such that both the arms are opposite to each other and forms a straight line then it is called a straight angle. The measure of a straight angle degree is 1800. Below is the straight angle diagram.

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From the above figure, OY and OX are the sides of the angle. And O is the vertex of the angle. The sides of the angle form 1800 with the line called a straight angle.

Two rays intersecting or meeting at a point form an angle. The point is said to be vertex and the rays are said to be the sides of an angle. The measurement between the two rays is measured in degrees. An angle is denoted by a single alphabet or three alphabets. For example, the below figure is represented as ∠ABC and called an angle ABC.

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Different Types of Angles

According to the different measures of an angle, an angle is divided into 6 different types.

  • Acute Angle

  • Obtuse Angle

  • Right Angle

  • Straight Angle

  • Reflex Angle

  • Full Angle

In this topic, we will study straight angles in detail. We will learn its definition, properties, and examples.


Properties of Straight Angles

Some important properties of straight angles are as follows:

  • In a straight angle, both sides of the angle are opposite to each other.

  • The straight angle completes half of the rotation.

  • The straight angle degree is 1800.

  • Straight angles can be formed by joining to right angles.

How to construct a Straight Angle Diagram?

The steps to construct a Straight Angle Diagram are as follows:

  • Draw a straight-line OA using a ruler, with O as the vertex of an angle

  • Now place the protractor on this line such that the baseline of the protractor is over OA. The point A should be at 00 of the protector.

  • Now starting from 0° move towards 180 degrees, On reaching 180°, mark a point B there.

  • Now join the points O and B. we get another side of an angle opposite to OA. thus forming a straight angle.

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Points to Remember:

  • The measure of a straight angle is always 1800.

  • When we move anticlockwise the straight angle measures + 1800.

  • When we move clockwise the straight angle measures - 1800.

  • The arms of an angle face opposite to each other.


Let us understand the concept of straight angle by straight angle examples


Solved Examples:

Example 1:

Identify the straight angle in the below figure. 

Solution: (image will be uploaded soon)

Angle BOD is a straight angle because it measures 1800, and it is formed by the addition of two right angles i.e. ∠COB + ∠COD = 1800. Also it forms a straight line.


Example 2: At what time is the angle between the hands of a clock exactly one straight angle?

Solution: At 6 o’clock.


Example 3: In the given figure, ∠AOB is a straight angle, ∠AOC = 68°, and ∠BOC = x°. 

Find the value of the x.

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Solution: As given that ∠AOC = 680 and ∠AOB is straight angle

We know that straight angle measures 1800

Therefore,

∠AOB  = ∠AOC  + ∠ BOC

1800 = 680. + x 

x = 180 - 68

x = 1120

Hence x = 1120


Example 4: In the given figure, ∠AOB  is a straight angle, ∠AOC = (3x+20)° and ∠ BOC =(4 x-36)°. Find the value of the x.

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Solution: 

As given that ∠AOC = (3x + 20)0 and ∠BOC = (4x - 36)0 and ∠AOB is straight angle

We know that straight angle measures 1800

Therefore,

∠AOB  = ∠AOC  + ∠ BOC

1800 = (3x + 20) . + ( 4x - 36) 

180 = 7x - 16

7x = 180 + 16

 x = 196/7

x = 28

Hence x = 280


Quiz Time

  1.  In the given figure , AOB is a straight angle, ∠ AOC = (3x-8)° and ∠COD =50 and ∠BOD° =(x+10)°. Find the value of the x.

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  1. Two angles form a straight angle. The measure of one of its angles is 62°. Find the other angle.


Fun Facts

  • The word angle was discovered from the Latin word of angulus, It means corner. 

  •  An angle was the space or interval between intersecting lines was supposed by Carpus of Antioch.

  • The straight is an angle which is equal to 1800 or ½ turn.

  • A perigon is also called a complete angle, or a full angle. It has 3600 or a complete 1 turn.

FAQ (Frequently Asked Questions)

1. Is a Triangle a Straight Angle?

Answer: No, a triangle cannot be a straight angle.

As we know that the sum of the measures of the angle of a triangle is 1800  and also from straight angle definition straight angle measures 1800, but we cannot consider a triangle as a straight angle because a triangle is an enclosed figure and a straight angle is in the form of a straight line.

Triangle is a closed figure with three sides and three vertices, while a straight angle has collinear points so that it cannot form a closed figure.

Hence a triangle and straight angle are different.

2. What are the Real-Life Straight Angle Examples?

Answer: Some of the straight angle examples are:

  • A plane inclined staircase forms a straight angle

  • The angle formed in a see-saw is straight.

  • Any flat surface has an angle of 1800.

  • A straight stick has a straight angle which is 1800.

  • A clock hand makes a straight angle at 6 o’clock.

3. What is Half of a Straight Angle?

Answer: According to straight angle definition an angle is a straight angle if it measures 1800. Half of the straight angle is 900, and which represents a right angle. Therefore half of a straight angle is the right angle. Two right angles can form a straight angle.

4. Is a Straight Angle a Reflex Angle?

Answer: According to straight angle definition an angle is a straight angle if it measures 1800. And according to reflex angle, an angle whose measure is greater than 1800 and less than 3600 is called a reflex angle. Therefore a straight angle is not a reflex angle.