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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 formed when two rays originate from a common endpoint called the vertex. The standard unit of measurement for an angle is degrees (∘^\circ). One complete revolution of a ray around its vertex represents an angle of 360∘360^\circ.

Anatomy of an angle showing vertex, rays, and the angle arc.
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Right Angle and Straight Angle: A right angle measures exactly 90∘90^\circ (one-quarter of a revolution), while a straight angle measures exactly 180∘180^\circ (half of a revolution).

Diagram showing a 90 degree right angle and a 180 degree straight angle.
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Acute and Obtuse Angles: An angle smaller than a right angle (<90∘< 90^\circ) is called an acute angle. An angle larger than a right angle but smaller than a straight angle (between 90∘90^\circ and 180∘180^\circ) is called an obtuse angle.

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Reflex Angle: An angle which is larger than a straight angle but less than a full revolution (between 180∘180^\circ and 360∘360^\circ) is called a reflex angle.

📐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.

Problem 3:

Identify the type of angle shown in the diagram which measures 135∘135^\circ.

An obtuse angle of 135 degrees.

Solution:

The angle measures 135∘135^\circ. Since 90∘<135∘<180∘90^\circ < 135^\circ < 180^\circ, it is an Obtuse Angle.

Explanation:

Any angle that lies between a right angle (90∘90^\circ) and a straight angle (180∘180^\circ) is classified as obtuse.

Problem 4:

Determine the type of the outer angle formed by the hands of a clock when the time is 4 o'clock, given the interior angle is 120∘120^\circ.

Clock face showing a reflex angle between the hands at 4 o'clock.

Solution:

The outer angle is 360∘−120∘=240∘360^\circ - 120^\circ = 240^\circ. Since 180∘<240∘<360∘180^\circ < 240^\circ < 360^\circ, the angle is a Reflex Angle.

Explanation:

A reflex angle represents the larger 'outside' turn between two rays when the interior angle is less than 180∘180^\circ.