How to Find a Reflex Angle in Maths (with Formula & Examples)
The concept of reflex angle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. You will find it in geometry, polygon properties, clocks, and competitive exams. Understanding reflex angles helps you quickly identify angle types in diagrams and solve questions more efficiently.
What Is Reflex Angle?
A reflex angle is defined as any angle that is greater than 180 degrees but less than 360 degrees. In other words, if an angle opens wider than a straight line (180°), but does not form a full circle (360°), it is called a reflex angle. You’ll find this concept applied in areas such as types of angles, rotational movements, and common clock positions.
Key Formula for Reflex Angle
Here’s the standard formula for finding a reflex angle:
\[ \text{Reflex Angle} = 360^\circ - \text{Given Angle} \]
Reflex Angles in Geometry
Reflex angles appear naturally in many geometric shapes and scenarios. For example, in a polygon with more than four sides (like a concave pentagon), one of the interior angles may be a reflex angle. On a clock, the larger angle created by the hour and minute hands (like at 7 o’clock) is a reflex angle.
| Where Found | How It Appears |
|---|---|
| Clock (e.g., 7 o’clock) | The larger sweep between the hour and minute hand forms a reflex angle. |
| Concave Polygon | A vertex that points inward has a reflex interior angle. |
| Protractor/Basics | An angle opening more than 180° but less than 360° on a circle. |
How to Find Reflex Angle: Step-by-Step Method
If you know the smaller (internal) angle in a figure or diagram, use these steps to find the reflex angle:
1. Note the given angle in your diagram (for example, 120°).2. Apply the formula: Reflex angle = 360° – given angle.
3. Subtract: 360° – 120° = 240°.
4. Answer: The reflex angle is 240°.
Reflex Angle Examples (With Solutions)
Let’s practice with typical exam questions involving reflex angles:
Example 1:If angle PQR = 82°, what is the reflex angle at Q?
1. Reflex angle = 360° – 82°
2. Reflex angle = 278°
Example 2:
Which of these is a reflex angle?
(a) 165° (b) 243° (c) 90° (d) 315°
1. Reflex angles are between 180° and 360°.
2. Both 243° and 315° are reflex angles.
Example 3:
On a clock, what is the reflex angle formed by the hands at 2 o’clock?
1. Shortest angle between hands = 60° (each hour = 30°)
2. Reflex angle = 360° – 60° = 300°
Example 4:
Is 180° a reflex angle?
1. Reflex angle must be greater than 180°.
2. So, 180° is not a reflex angle—it is a straight angle.
Reflex Angle vs. Obtuse Angle
Many students confuse obtuse and reflex angles. Here’s a comparison to clarify:
| Property | Obtuse Angle | Reflex Angle |
|---|---|---|
| Range | 91° to 179° | 180° to 359° |
| Looks Like | Less than a straight line | More than a straight line, less than a circle |
| Mnemonic | "Ob" = "Over (90° but under 180°)" | "Reflex" = "Reaching Further (past 180°)" |
Reflex Angles in Real Life
You can find reflex angles all around you! Here are some common examples:
- Clock hands from 12 to 7 (or similar positions)
- The angle of a steering wheel turned past halfway
- Swings or doors opened beyond a straight line
- Field markings in sports (corner arc in soccer)
- Art and design patterns with curves over 180°
Speed Tip for Exams: Reflex Angle Shortcuts
A quick shortcut: If an exam question warns you the angle is “external” or “the other side,” it’s likely talking about a reflex angle! Always subtract the given angle from 360° for the answer.
Trick: If a diagram shows multiple angles at a point, check which is “inside” (acute, right, or obtuse) and which is “outside” (reflex). Practice with angle measurement tools for accuracy.
Try These Yourself
- Find the reflex angle if the interior angle is 153°.
- Is 220° a reflex angle or not?
- Draw a shape with a reflex angle inside it.
- In which direction do the clock hands form a reflex angle at 9 o’clock?
Frequent Errors and Misunderstandings
- Confusing right, obtuse, and reflex angles, especially in diagrams.
- Forgetting that a reflex angle is NOT 180° or 360°, but strictly between.
- Accidentally using 180° addition or subtraction instead of 360° for calculation.
- Misidentifying the “outside angle” as “not part of the shape.”
Relation to Other Concepts
Reflex angles are related to supplementary angles, obtuse angles, and understanding types of polygons. Mastering reflex angles also strengthens your knowledge for angles in degrees and complex geometric constructions.
Classroom Tip
To quickly spot a reflex angle, look for the “bigger slice” at a point or where a line “wraps around.” Remember: if it looks wider than a straight line but doesn’t complete the circle, it’s reflex. Vedantu’s tutors use animated diagrams to make this visual cue stick!
We explored reflex angles—from definition, formula, common mistakes, and real-life connections. With practice, you’ll be able to easily identify reflex angles in any diagram or exam question. Continue learning with Vedantu for more tips, tricks, and interactive examples on angle types and geometry basics.
FAQs on Reflex Angle Explained – Definition, Formula, Comparison & Examples
1. What is a reflex angle in Maths?
A reflex angle in mathematics is an angle that measures more than 180° but less than 360°. It's larger than a straight angle (180°) but smaller than a full circle (360°). Think of it as the larger angle formed when two lines intersect.
2. How do you calculate a reflex angle if the interior angle is given?
To find a reflex angle, subtract the measure of the given interior angle from 360°. The formula is: Reflex Angle = 360° - Interior Angle. For example, if the interior angle is 60°, the reflex angle is 360° - 60° = 300°.
3. Where are reflex angles found in daily life?
Reflex angles are all around us! You can find them in the hands of a clock (e.g., the angle between the hands at 8 o'clock), the rotation of a wheel, the swing of a door opening beyond 180°, and in various architectural designs.
4. How are reflex and obtuse angles different?
An obtuse angle measures more than 90° but less than 180°. A reflex angle is much larger, measuring more than 180° but less than 360°. The key difference is their size; a reflex angle is always greater than an obtuse angle.
5. Can an angle of 270° be called a reflex angle?
Yes, an angle of 270° is a reflex angle because it falls within the range of a reflex angle (greater than 180° and less than 360°).
6. What is the difference between a reflex angle and its corresponding angle?
A reflex angle and its corresponding angle are supplementary angles that add up to 360°. The corresponding angle is the smaller angle that shares the same vertex and arms as the reflex angle.
7. How do I draw a reflex angle using a protractor?
First, find the corresponding angle by subtracting the reflex angle measure from 360°. Draw the corresponding angle using a protractor. The larger angle formed outside of the drawn angle is your reflex angle.
8. Can a triangle have a reflex angle?
No, a triangle cannot have a reflex angle. The sum of interior angles in any triangle always equals 180°, and a reflex angle is greater than 180°.
9. Can a quadrilateral have a reflex angle?
Yes, a concave quadrilateral (a quadrilateral with at least one interior angle greater than 180°) can have a reflex angle. A convex quadrilateral cannot have a reflex angle, as all its interior angles must be less than 180°.
10. What are some real-world examples of reflex angles besides clocks?
Examples include: the path of a swing, the movement of a spinning top, the arc of a circular saw blade, and certain architectural features like curved roofs or arches.
11. How are reflex angles used in geometry?
Reflex angles are crucial in understanding polygon properties, particularly concave polygons. They're also relevant when studying rotations and transformations in geometry.
12. What are some common mistakes students make when identifying reflex angles?
Common mistakes include confusing reflex angles with obtuse angles, incorrectly measuring angles using a protractor, and failing to visualize the larger angle in diagrams.
