## What Is a 30 Degree Angle?

**A 30 degree angle is an ****acute angle**** whose ****angle measure**** is exactly 30 degrees. It is an angle obtained by bisecting a 60 degree angle.**

An angle is a geometric figure formed when two rays meet at a common point called the vertex.

#### Begin here

## What Does a 30 Degree Angle Look Like?

Observe the given diagram. Here, two rays PB and PD form a 30 degree angle at the vertex P.

#### Related Worksheets

## How to Construct a 30 Degree Angle with a Protractor

A protractor is a geometric instrument used to measure and construct angles. Here’s a step-by-step guide to construct a 30 degree angle using a protractor:

**Step 1**: Draw a line segment AB. Align the center of the protractor with the vertex A. Baseline of the protractor is aligned with the line segment AB.

**Step 2**: Mark the 30 degree angle on the inner scale that starts from 0 on the right side. Name this point as C.

**Step 3: **Remove the protractor and join the line AC.

## How to Construct a 30 Degree Angle with a Compass

Step 1: Draw a ray AB. Keeping A as center and with a suitable radius on the compass, draw an arc on the ray AB that touches the ray AB at the point P. | Step 2: With P as the center and keeping the same radius, draw an arc that cuts the previous arc atpoint Q. |

Step 3: With P and Q as centers, draw two arcs that intersect each other at point E. | Step 4: Join points A and R through a straight line. Label this line as AR. ∠RAB=30 |

## Negative 30 Degree Angle

When the initial arm is rotated clockwise to form an angle, the angle is negative.

## 30 Degree Angle in Real Life

There are 12 divisions in an analog clock. Each division represents a central angle of 30 degrees. If you cut a pizza into 12 equal parts, each part represents a central angle of 30 degrees.

## Facts about 30 Degree Angle

- The 30 degree angle is one-third of the right angle.
- The complement of a 30 degree angle is a 60 degree angle.
- Six 30 degree angles make a straight angle.
- Twelve 30 degree angles make a complete angle.

## Conclusion

In this article, we learned about the 30 degree angle. We discussed how to construct a 30 degree angle using i) protractor and ii) compass. Let’s solve a few examples and practice MCQs based on the concept of 30 degree angle.

## Solved Examples on 30 Degree Angle

**Example 1: How many 30 degree angles make a right angle?**

**Solution**:

$\frac{90^{\circ}}{30^{\circ}} = 3$

Three 30 degree angles make a right angle.

**Example 2: Convert 30 degrees to radians.**

**Solution:**

Let’s convert 30 degrees into radians.

Angle in radians = Angle in degrees $\times \frac{\pi}{180^{\circ}}$

Angle in radians $= 30^{\circ} \times \frac{\pi}{180^{\circ}} = \frac{\pi}{6}$

So, the 30 degree angle in radians is $\frac{\pi}{6}$.

**Example 3: Construct a 30 degree angle by bisecting a 60 degree angle.**

**Solution:**

Consider a 60 degree angle with vertex O.

Keeping the compass at the vertex O and with suitable radius, draw an arc intersecting both the arms of the given 60 degree angle at points A and B.

Taking A and B as centers and keeping the radius length more than half of AB, draw two arcs that intersect each other at the point C.

Join O and C.

Here, ∠AOB = 30^{o}

∠AOC = ∠BOC = 30^{o}

## Practice Problems on 30 Degree Angle

## 30 Degree Angle - Construction With Compass and Protractor, Examples

### The 30 degree angle is

The 30 degree angle is an acute angle.

### What is a 90 degree angle called?

The 90 degree angle is called the right angle.

### hat angle will be obtained on the bisection of a 30-degree angle?

Bisection of the angle means dividing it into two halves. Hence, half of the 30 degree angle is a 15 degree angle.

## Frequently Asked Questions about 30 Degree Angle

**What are acute angles?**

**Acute angles are angles that measure less than 90 degrees.**

**Is the 30 degree angle an obtuse angle?**

The 30 degree angle is not an obtuse angle. It is an acute angle.

**What is the value of **30** angle in terms of pi?**

$30^{\circ} = \frac{\pi}{6}$

**How do you measure 30 degrees without a protractor?**

To measure 30 degrees without a protractor, you can use a simple method. Draw a straight line, then create a perpendicular line from it. The angle formed where the two lines meet is 90 degrees. Now, bisect this angle by drawing a line from the intersection point, and the angle between the two lines will be 30 degrees.