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

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## 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

## 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.

## 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.

## 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 = 30o

∠AOC = ∠BOC = 30o

## Practice Problems on 30 Degree Angle

1

### The 30 degree angle is

an obtuse angle
an acute angle
a reflex angle
a straight angle
CorrectIncorrect
Correct answer is: an acute angle
The 30 degree angle is an acute angle.
2

### What is a 90 degree angle called?

Acute angle
Obtuse angle
Straight angle
Right angle
CorrectIncorrect
The 90 degree angle is called the right angle.
3

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

60 degree angle
15 degree angle
30 degree angle
45 degree angle
CorrectIncorrect
Correct answer is: 15 degree angle
Bisection of the angle means dividing it into two halves. Hence, half of the 30 degree angle is a 15 degree angle.

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