Reflex Angle in Geometry

Reflex Angle is one of the many types of angles introduced in geometry, characterized by its measurement between 180° and 360°. Geometry is a branch of mathematics that deals with the study of shapes, sizes, and positions of objects in space. Angles are a fundamental concept in geometry that helps us describe and understand the relationships between lines, segments, and shapes. 

However, one type of angle that often confuses students is the reflex angle. A reflex angle is identified by their measurements which is greater than 180° but less than 360°. A reflex angle is characterized by its wide opening, typically spanning more than half of a circle. In other words, it typically resembles the ‘C’ shape or is more extended than that.

Here, we will explore more about a reflex angle, real-life examples of reflex angle, reflex angle comparison with other angles such as right angle, acute angle, obtuse angle, zero angle, and more. The blog will also provide information on applications of reflex angle, and properties of the reflex angle. Let’s first understand what is the definition of a Reflex Angle.

What is a Reflex Angle?

A reflex angle is a type of angle that measures more than 180° but less than 360°. It is an angle that turns more than halfway around a circle. In simpler terms, a reflex angle is an angle that is bent backwards beyond a straight line but doesn’t complete a full process (which is 360°).

Reflex Angle Definition

A reflex angle is an angle that measures greater than 180° but less than 360°.

Degree Measure of Reflex Angles

Some degree examples of reflex angle (greater than 180° and less than 360°):

• 190°
• 215°
• 275°
• 330°
• 340°

Reflex Angle Examples in Real-Life

Let’s understand some common examples of a reflex angle:

• A wall clock showing 3:40 with an hour hand pointing towards 3 and the minute hand pointing towards 40.
• A reflex angle can be formed between the two arms of a protractor.
• A reflex angle can be formed when the blades of a fan are spinning.
• A reflex angle can be formed between the two blades of a pair of scissors.

Reflex Angle in Clock

As there are two hands on any analog clock, and these hands can display all possible angles between them, in both clockwise and counterclockwise directions. These hands can represent angles such as straight angles, complete angles, acute angles, obtuse angles, and right angles. For reflex angles, we can observe the following examples:

• Imagine the hour hand pointing at 3 and the minute hand pointing at 9 on a clock. The angle between them is 270 degrees, which is a reflex angle because it’s greater than 180 degrees.
• Another example is when the hour hand is at 2 and the minute hand is at 8. The angle formed between them is 250 degrees, which is also a reflex angle.

Read More,

• Right Angle
• Straight Angle

How to Measure a Reflex Angle?

Follow the steps below to measure a reflex angle:

Step 1: Place the center of the protractor at the vertex of the angle.

Step 2: Align one arm of the protractor counterclockwise with one of the rays forming the angle.

Step 3: Read the degree marking at the end of the second ray. This measure is the size of the relfex angle.

How to Draw a Reflex Angle?

To draw a reflex angle, follow the below-mentioned steps:

Step 1: Prepare your drawing tools such as pencil, eraser, a piece of paper, etc.

Step 2: Draw a straight line with a ruler to set the base of a reflex angle.

Step 3: Draw a point or vertex at one end of the straight line and extend one ray from the vertex.

Step 4: Measure the reflex angle, which should be greater than 180° but less than 360°.

Step 5: Draw the second ray to complete the reflex angle.

Step 6: Label all the measurements, remove the extra lines and markings, and fill the shade in a reflex angle formed.

Comparison of Reflex Angle with Other Angles

Here’s a comparison between reflex angle and other types of angles i.e acute, obtuse, straight, full circle, and right angle:

Aspect	Reflex Angle	Acute Angle	Obtuse Angle	Straight Angle	Complete Angle	Right Angle
Measurement	Greater than 180° but less than 360°	Less than 90°	Between 90 and 180°	It is exactly 180°	It measures complete 360°	It is exactly 90°
Description	More than a straight line	Narrower than a right angle	More than a right angle but less than a reflex angle	More than a right angle but less than a reflex angle	Complete a full rotation around a point	It is a ‘L’ shaped angle. Also, known as a perpendicular angle

Learn More about Types of Angles and Types of Triangles.

Properties of Reflex Angle

There are several properties of a reflex angle which define their characteristic. Below we have listed some of the properties of a reflex angle:

• A reflex angle measures greater than 180° and less than 360°. In mathematical notation, a reflex angle can be expressed as:
  • 180° < Reflex Angle <360°
• The sum of a reflex angle and an adjacent acute or obtuse angle (either of which can be either interior or exterior) will always equal 360°. This property is known as the ‘angle sum property of a circle.
• In mathematical terms, if A is a reflex angle, and B is an adjacent angle (interior or exterior), then B is an adjacent angle (interior or exterior), then A + B = 360°
• Reflex angles have a wide opening, spanning more than half of a circle. They appear “bent” or “folded” in shape and are often greater than a straight angle (180°)

Read More,

• Parallel Lines
• Pythagoras Theorem
• Perpendicular Lines

Applications of Reflex Angle

There are several applications of a reflex angle such as navigation, surveying and geodesy, robotics, structural engineering, physics, art and design, etc. Below we have discussed all of these in detail:

• In navigation, particularly in aviation and maritime contexts, reflex angles are used to calculate headings, bearings, and course changes
• Surveyors and geodesists use reflex angles when measuring and mapping the Earth’s surface
• In robotics, reflex angles are important in robot kinematics. Engineers use them to describe the configuration of robot arms and joints
• Architects and structural engineers may encounter reflex angles when designing buildings or structures with irregular shapes
• Artists and graphic designers use reflex angles in their work to create abstract or visually striking compositions

Solved Problems on Reflex Angle

Problem 1: What is the reflex angle of 110°?

Solution:

To find a reflex angle of any given angle, you need to subtract the given angle from 360°. The reflex angle of 110° is solved below:

360° – 110° = 250°

Therefore, a reflex angle of 110° is 250°.

Problem 2: If ∠AOB = 57°, then find out the size of reflex ∠AOB.

Solution: 

A reflex angle and its corresponding angle are always below 360°. 

Therefore, reflex angle AOB = 360° − 57° = 303°.

Problem 3: Find the measure of an angle which is complementary to 35°.

Solution:

If the sum of two angles is equal to 90° then they are called complementary angles.

Let ‘a’ be the angle which is complementary to 35°.

So, a + 35° = 90°

a = 90 – 35

a = 55°

Therefore, the required angle is 55°.

Problem 4: Are 120° and 55° are supplementary angles?

Solution: 

If the sum of two angles is 180° then they are called supplementary angles.

Given angles are 120° and 55°

Sum of 120° and 55° is 175°

Therefore, 120° and 55° are not supplementary angles.

Problem 5: If 4x + 28° and 6x – 16° are congruent, then find the value of x.

Solution:

Congruent angles are also known as equal angles.

So, 4x + 28° = 6x – 16°

6x – 4x = 28 + 16

2x = 44

x = 22°

Therefore, the value of x is equal to 22°

Practice Problems on Reflex Angle

Problem 1: A wall clock reads 3:30. Calculate the measure of the reflex angle formed by the hour and minute hands.

Problem 2: Are 46° and 55° complementary angles?

Problem 3: Are 135° and 60° supplementary angles?

Problem 4: If 36° and 4x + 12° form a right angle, then find the value of x.

Problem 5: Classify the following angles:

• 175°
• 62°
• 330°
• 129°
• 190°

Problem 6: If three angles 3x, 5x and x together form a straight angle, find the angles.

Reflex Angle – FAQs

1. What are Reflex Angles?

A reflex angle is a type of angle that measures more than 180° but less than 360°. It is an angle that turns more than halfway around a circle. In simpler terms, a reflex angle is an angle that is bent backward beyond a straight line but doesn’t complete a full circle (which is 360°).

2. What are the 7 Types of Angle?

There are seven types of angles commonly used on Maths:

• Acute Angle
• Right Angle
• Zero Angle
• Straight Angle
• Reflex Angle
• Complete Angle
• Right Angle

3. What is the Measure of Reflex Angle?

A reflex angle is a type of angle that measures more than 180° but less than 360°.

4. What is a Reflex Angle of 36°?

To find the reflex angle of 36 we need to substract the given from 360°

360° – 36° = 324°

Therefore, reflex angle of 36 is equal to 324°.

5. How to Find a Reflex Angle?

To find a reflex angle, follow these steps:

1. Measure the reflex angle.
2. Vertify the measurements.
3. Check if it ‘bend backwards’ or goes beyond a straight line, then it is confirmed that it is a reflex angle.
4. Label the measurements of the angle.

6. What is a Reflex Angle in clock?

A reflex angle in clock can be explained with the following example.

• A wall clock showing 3:40 with an hour hand pointing towards 3 and the minute hand pointing towards 40. This position is a reflex angle, when measured in counter clock wise.

7. How to Measure a Reflex Angle with a Protractor?

To measure any reflex angle with protractor, we can use following steps:

1. Place the center of the protractor at the vertex of the angle.
2. Align one arm of the protractor counterclockwise with one of the rays forming the angle.
3. Read the degree marking at the end of the second ray. This measure is the size of the relfex angle.

8. What is a Reflex Angle in Math?

In math, a reflex angle is a type of angle that measures more than 180° but less than 360°.