30 degree angle

30 degree angle
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In this mini-lesson, we will learn about 30-degree angle by understanding the rules to draw it using a protractor, its real-life examples, and how to apply them while solving problems. We will also discover interesting facts around them.

Have you ever noticed triangular shapes in your surroundings?

Did you know that if we divide the 60-degree angle into two parts, we have a 30-degree angle?

30-degree angles have a very significant role in real-life applications.

For example, there is a 30-degree rule in film making. Cameramen have to place the camera at 30 degrees with respect to the ground to capture more beautiful photos and videos.

In this mini-lesson, let us explore the 30-degree angle!

30 degree cinema rule

Lesson Plan

What Is a 30-Degree Angle?

An angle is formed when two rays meet at a point.

The point of intersection of the ray OA and ray OB is O, which is called the vertex.

angle in math

If the measure of the angle formed by two rays is 30 degrees, then the angle is called a 30-degree angle.

The angle formed by the ray OA and OB is written as \(\angle \text{AOB}\) or \(\angle \text{BOA}\).

30-degree angle

\[\angle \text{AOB} = \angle \text{BOA} = 30^{\circ}\]

How to Construct a 30-Degree Angle Using a Protractor?

In this section, let us explore how to construct a 30-degree angle with the help of a protractor.

Follow the given steps:

Step 1: Draw a line segment \(OA\).

Step 2: Place the center tip of the protractor at point \(O\) such that the protractor perfectly aligns with line AO.

correct way to place the protractor

Step 3: Start from 0 on the protractor in the clockwise direction and stop at 30. Mark point D.
If point A lies to the right of O, then start measuring anticlockwise and stop at 30

constructing 30 degree angle

Step 4: Join the point D with O. The \(\angle \text{AOC} = 30^{\circ}\) is the required angle.

constructing 30 degree angle

Click on the Go button to understand the process of construction of a 30-degree angle using a protractor with the help of animation.

What Are 30-Degree Angles in Real Life?

The 30-degree angle can be seen in many objects around us.

The hands of an analog clock at 1:00 PM forms an angle of 30 degrees. 

30-degree angle on a clock

If many friends come to your house and you need to cut the pizza into 12 slices, each slice of the pizza has a 30-degree angle.

30-degree angle on a pizza slice

Sometimes, the scissors we use to cut paper and cloth makes a 30-degree angle.

30-degree angle on scissors

Have you ever gone for a cycle ride with your friends and observed that the roads are diverging at some angles. Those angles could be 30-degree angles. 

30-degree angle on road

Thinking out of the box
Think Tank
  1. How many 30-degree angles are there in a
    a) Straight angle
    b) Complete angle

Solved Examples

Example 1



In the \(\triangle \text{ABC}\), use a protractor to measure \(\angle \text{CAB}\).

An example of a triangle


Place the protractor's baseline along the line \(\text{AB}\) and the center of the protractor at the vertex \(\text{A}\).

Observe the reading in the protractor which overlaps with line \(\text{AC}\).

 Measure of angle A of a triangle ABC

\(\therefore \angle \text{CAB} = 30^\circ\) 
Example 2



Mathew ordered a large pizza at his home. Some time later, few of his friends came to his house. Mathew called the pizza shop and asked them to cut the pizza such that he would get 25% of the pizza and each of his friends would get a piece with a 30-degree angle. If each friend got one piece, how many friends came to Mathew's place?

angle on a pizza


The pizza is circular; hence the total angle of the pizza is \({\text{360}}^{\circ}\).

Mathew is eating 25% of the pizza.

\[= \text{25% of } {\text{360}}^{\circ} \\[0.2cm]
= \dfrac{25}{100} \times {\text{360}}^{\circ} \\[0.2cm]
= \dfrac{1}{4} \times {\text{360}}^{\circ} \\[0.2cm]
= {\text{90}}^{\circ}\]

Mathew is eating a piece with \({\text{90}}^{\circ}\) angle.

The remaining pizza will be distributed among his friends equally.

\[{\text{360}}^{\circ} - {\text{90}}^{\circ} = {\text{270}}^{\circ}\]

Now, Mathew's friends will eat \({\text{270}}^{\circ}\) pizza.

Each pizza slice has an angle of 30 degrees.

Therefore, total number of friends that came at Mathew's house are 

\[= \dfrac{\text{Total angle of pizza remaining}}{\text{Angle of each slice}} \\[0.2cm]
= \dfrac{\text{270}}{30} \\[0.2cm]
= 9\]

\(\therefore \text{9 friends came at Mathew's house.}\)
important notes to remember
Important Notes
  1. Another unit used to measure angles is radians.
    \(pi\) radians = \(180^\circ\)
  2. \(30^\circ\) in radians is \(\dfrac{\pi}{6}\).
  3. The sum of all the angles of a triangle is \({\text{180}}^{\circ}\).
  4. The 30-degree angle is an acute angle.

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.


Let's Summarize

The mini-lesson targets the fascinating concept of 30-degree angle. The math journey around 30-degree angle starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that is not only relatable and easy to grasp, but will also stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!
Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.
Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

Frequently Asked Questions(FAQs)

1. What type of angle is 30 degrees?

A 30-degree angle is an acute angle because it is less than 90 degrees.

2. How do you draw a 30-degree angle with a protractor?

To draw a 30-degree angle using the protractor, follow these steps.

Step 1: Draw a line segment \(OA\).

Step 2: Place the center tip of the protractor at the point \(O\) such that the protractor perfectly aligns with line AO.

Step 3: Start from 0 on the protractor in the clockwise direction and stop at 30. Mark the point D.

Step 4: Join the point D with O. \(\angle \text{AOC} = 30^{\circ}\) is the required angle.

3. How many 30-degree angles does it take to make a full turn?

A full turn is 360°.

Since \(30 \times 12 = 360\), therefore there are twelve 30-degree angles in a full turn.

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