[Maths Class Notes] on Straight Angle Pdf for Exam

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.

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.

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.

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.

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.