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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.