180 Degree Angle – Definition, Construction, Facts, Examples, FAQs

Home » Math Vocabluary » 180 Degree Angle – Definition, Construction, Facts, Examples, FAQs

What Is a 180 Degree Angle?

The 180 degree angle is an angle that forms a straight line. The 180 degree angle in radians is or about 3.14 radians.

180 degree angle

You can see that the straight line is formed when the two arms of the angle (BA and BC) are opposite rays. The two arms extend in the opposite directions. Thus, the 180 degree angle is also called ‘a straight angle.’

How to Draw a 180 Degree Angle

There are two methods to draw an accurate 180 degree angle: using a compass or using the protractor.

Constructing 180 Degree Angle Using Protractor

Step 1: Draw ray OA. Align the center of the protractor with the point O. O will be the vertex of the angle.

Step 2: Mark the 180 degree reading (on inner calibration) as point B.

Step 3: Join OB.

∠AOB = 180o

Constructing a 180 degree angle using a protractor

Constructing 180 Degree Angle Using Compass

Here are the steps to assist you in drawing 180 degree angle using a compass: 

Step 1: Draw a straight line and name it PQ.

Step 2: Mark a point between PQ using a dot and name it as O.

Step 3: Place the compass on the point O and make an arc that starts on OQ and ends on OP, making a semicircle.

Step 4: Name the points of intersection of the arc with OP and OQ as X and Y respectively. 

∠YOX = 180o

Construction of 180 degree angle using compass

Negative 180 Degree Angle

The straight angle if measured clockwise is a negative straight angle (-180o).

Negative 180 degree angle

180 Degree Angle Name

As we mentioned earlier, the 180 degree angle forms a straight line. So, it is also known as a “Straight angle” or“flat angle.”

Types of angles formed by a 180 degree angles:

  • Half of 180o angle measures 90o. It is known as a right angle.
  • Twice the 180o angle measures 360o. It is known as a complete angle or a full angle.
  • Angles greater than 180o and less than 360o are called reflex angles.
  • Angles between 90o and 180o are called obtuse angles.

Facts about 180 Degree Angle

  • Two angles which add up to 180 degrees are called supplementary angles. 
  • Angles in a linear pair always add up to 180 degrees.
  • The sum of three angles in a triangle is 180 degrees because if you line them up they form a straight line.
  • The hands of the clock make 180 degrees 22 times in a day.
  • Hands of a clock make a 180 degree angle at 2:45, 6:00 and 12:30.
  • The straight angle is half of the complete revolution.

Conclusion

In this article, we learned about the 180 degree angle (straight angle), and its construction using protractor and compass. Let’s solve a few examples and practice problems based on the concept of 180 degree angle.

Solved Examples on 180 Degree Angle

Example 1: What is the measure of the angle BOC?

Finding missing angle

Solution: 

The straight angle is 180 degrees. Thus, two angles making a straight angle will add up to 180 degrees.

Here, ∠AOB =  40o

Let us assume that  ∠BOC = x. 

x + 40o = 180o

x = 180o – 40o

x = 140o

Example 2: How is 180 degree angle related to a complete angle and a right angle? 

Solution: 

A complete angle measures 360 degrees. 

Half of the complete circle angle is 180 degree angle.

 Right angle measures 90 degrees.

Twice the right angle is a straight angle. Two adjacent right angles form a straight angle.

Two adjacent right angles make a straight angles

Example 3: What is the angle made by the hour hand and the minute hand when the clock reads 06:00?

Solution: 

Clock reading 06:00

Practice Problems on 180 Degree Angle

180 Degree Angle - Definition, Construction, Facts, Examples, FAQs

Attend this quiz & Test your knowledge.

1

Which angle measures 180 degrees?

Right angle
Straight angle
Obtuse angle
Acute angle
CorrectIncorrect
Correct answer is: Right angle
A 180 degree angle is a straight angle.
2

What does a 180 angle look like?

triangle
circle
a ray
a straight line
CorrectIncorrect
Correct answer is: a straight line
A 180 degree angle forms a straight line.
3

A straight angle is half the

right angle
complete angle
270 degree angle
reflex angle
CorrectIncorrect
Correct answer is: complete angle
A straight angle is half the complete angle.
4

What is the measurement of a 180 degree angle in radians?

$\pi$
$\frac{\pi}{2}$
$2 \pi$
$\pi$
CorrectIncorrect
Correct answer is: $\pi$
$180^{\circ} = \pi$ radians

Frequently Asked Questions about 180 Degree Angle

The 180 degree angle forms a straight line. Its arms form opposite rays.

  • Angles in a linear pair
  • Three interior angles of a triangle
  • Two supplementary angles

Yes, you can join two right angles to form a 180 degree angle.

A complete angle or a full angle is 360 degree angle.