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Understanding Elementary Shapes - Types of Angles (Right, Straight, Acute, Obtuse, Reflex)

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An angle is the measure of rotation between two rays that meet at a common endpoint called the vertex. Visualise it as the space between two clock hands or the opening of a pair of scissors.

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A Right Angle is an angle of exactly 90∘90^\circ. It looks like the corner of a square or the letter 'L'. It represents exactly 14\frac{1}{4} of a full revolution.

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A Straight Angle is an angle of exactly 180∘180^\circ. Visually, it forms a perfectly straight line and is equivalent to two right angles placed side-by-side. It represents 12\frac{1}{2} of a full revolution.

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An Acute Angle is any angle that measures more than 0∘0^\circ but less than 90∘90^\circ. These angles appear 'sharp' and are narrower than a right angle, like a partially opened book.

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An Obtuse Angle is an angle that measures more than 90∘90^\circ but less than 180∘180^\circ. It appears 'wide' and is larger than a right angle but smaller than a straight line, similar to the slope of a reclining chair.

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A Reflex Angle is an angle that is greater than 180∘180^\circ but less than 360∘360^\circ. This is the 'outer' angle formed when you look at the larger turn between two lines; it looks like a straight line that has been bent backwards.

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A Complete Angle or a Full Revolution measures exactly 360∘360^\circ. This happens when a ray rotates all the way around and returns to its original position, forming a full circle.

📐Formulae

1 Right Angle=90∘1 \text{ Right Angle} = 90^\circ

1 Straight Angle=180∘=2×90∘1 \text{ Straight Angle} = 180^\circ = 2 \times 90^\circ

1 Full Revolution=360∘=4×90∘1 \text{ Full Revolution} = 360^\circ = 4 \times 90^\circ

Acute Angle:0∘<θ<90∘\text{Acute Angle}: 0^\circ < \theta < 90^\circ

Obtuse Angle:90∘<θ<180∘\text{Obtuse Angle}: 90^\circ < \theta < 180^\circ

Reflex Angle:180∘<θ<360∘\text{Reflex Angle}: 180^\circ < \theta < 360^\circ

💡Examples

Problem 1:

Classify the following angles based on their magnitudes: (i) 75∘75^\circ (ii) 195∘195^\circ (iii) 90∘90^\circ (iv) 160∘160^\circ.

Solution:

Step 1: 75∘75^\circ is between 0∘0^\circ and 90∘90^\circ, so it is an Acute Angle. \ Step 2: 195∘195^\circ is between 180∘180^\circ and 360∘360^\circ, so it is a Reflex Angle. \ Step 3: 90∘90^\circ is exactly a Right Angle. \ Step 4: 160∘160^\circ is between 90∘90^\circ and 180∘180^\circ, so it is an Obtuse Angle.

Explanation:

To classify angles, we compare the given numerical degree measure against the standard range definitions for acute, right, obtuse, and reflex angles.

Problem 2:

A clock hand moves from 1212 to 99 in a clockwise direction. Find the fraction of the revolution it has completed and the name of the angle formed.

Solution:

Step 1: A full revolution covers 1212 hours on a clock. \ Step 2: Moving from 1212 to 99 covers 99 hours. \ Step 3: The fraction of revolution is 912=34\frac{9}{12} = \frac{3}{4}. \ Step 4: Calculate the degree measure: 34×360∘=270∘\frac{3}{4} \times 360^\circ = 270^\circ. \ Step 5: Since 180∘<270∘<360∘180^\circ < 270^\circ < 360^\circ, the angle is a Reflex Angle.

Explanation:

We first find what part of the total circular path (1212 hours) the hand has traveled, then convert that fraction into degrees to identify the angle type.

Types of Angles (Right, Straight, Acute, Obtuse, Reflex) Revision - Class 6 Maths CBSE