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Reflex Angle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Reflex AngleReflex Angle: Definition and ExamplesTable of ContentsReflex Angle: Definition, Examples, and Solutions Definition of Reflex Angle

A reflex angle is defined as an angle that is greater than 180∘180^{\circ}180∘ (a straight angle) but less than 360∘360^{\circ}360∘ (a complete angle). Every reflex angle has a corresponding angle that lies on the other side of it, and together they form a complete angle of 360∘360^{\circ}360∘. This corresponding angle can be an acute angle, obtuse angle, or a right angle.

Reflex angles can also be understood in relation to a straight angle. A reflex angle equals the sum of 180∘180^{\circ}180∘ and another angle, which may be acute, obtuse, or right. For example, 210∘=180∘+30∘210^{\circ} = 180^{\circ} + 30^{\circ}210∘=180∘+30∘ (an acute angle), 290∘=180∘+110∘290^{\circ} = 180^{\circ} + 110^{\circ}290∘=180∘+110∘ (an obtuse angle), and 270∘=180∘+90∘270^{\circ} = 180^{\circ} + 90^{\circ}270∘=180∘+90∘ (a right angle).

Examples of Reflex Angles Example 1: Finding the Corresponding Reflex Angle Problem:

What is the corresponding reflex angle of 160160160 degrees?

Step-by-step solution: Step 1, Recall that a reflex angle and its corresponding angle add up to 360∘360^{\circ}360∘. Step 2, Set up the equation: 160∘+reflex angle=360∘160^{\circ} + \text{reflex angle} = 360^{\circ}160∘+reflex angle=360∘. Step 3, Solve for the reflex angle: reflex angle=360∘−160∘=200∘\text{reflex angle} = 360^{\circ} - 160^{\circ} = 200^{\circ}reflex angle=360∘−160∘=200∘.

Therefore, the reflex angle corresponding to 160160160 degrees is 200∘200^{\circ}200∘.

Example 2: Identifying Reflex Angles Problem:

Identify reflex angles among: a) 140∘140^{\circ}140∘ b) 30∘30^{\circ}30∘ c) 300∘300^{\circ}300∘

Step-by-step solution: Step 1, Remember that reflex angles are greater than 180∘180^{\circ}180∘ but less than 360∘360^{\circ}360∘. Step 2, Check each angle against this definition:

a) 140∘140^{\circ}140∘ is between 90∘90^{\circ}90∘ and 180∘180^{\circ}180∘, so it's an obtuse angle, not a reflex angle.

b) 30∘30^{\circ}30∘ is less than 90∘90^{\circ}90∘, so it's an acute angle, not a reflex angle.

c) 300∘300^{\circ}300∘ is greater than 180∘180^{\circ}180∘ but less than 360∘360^{\circ}360∘, so it is a reflex angle.

Therefore, among the given angles, only 300∘300^{\circ}300∘ is a reflex angle.

Example 3: Clock Angles Problem:

What is the measure of angles made by the hands of a clock at 5:005:005:00?

Clock Angles

Step-by-step solution: Step 1, Understand that a clock face has 121212 divisions, making a complete circle of 360∘360^{\circ}360∘. Step 2, Calculate how many degrees each division represents: 360∘12=30∘\frac{360^{\circ}}{12} = 30^{\circ}12360∘​=30∘ per division. Step 3, At 555 o'clock, the hour hand points to 555 and the minute hand points to 121212. Step 4, Count the number of divisions between the hands: 555 divisions. Step 5, Calculate the angle between the hands: 5×30∘=150∘5 \times 30^{\circ} = 150^{\circ}5×30∘=150∘, which is an obtuse angle. Step 6, Find the reflex angle by subtracting from 360∘360^{\circ}360∘: 360∘−150∘=210∘360^{\circ} - 150^{\circ} = 210^{\circ}360∘−150∘=210∘.

Therefore, at 5:005:005:00, the clock hands form a reflex angle of 210∘210^{\circ}210∘.

Comments(2)JJewelryDesignerZachNovember 4, 2025This glossary page on reflex angles is great! It helped my students grasp the concept easily with those clear examples. Thanks!

MCMs. CarterSeptember 17, 2025This page explained reflex angles so clearly! I used the clock angle example to help my kids visualize it, and they totally got it. Great resource for teaching tricky concepts!

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