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Lines and Angles - Angle

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 rays are known as the arms of the angle.

Anatomy of an angle showing vertex and arms.
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Angles are classified based on their magnitude. A Right Angle is exactly 90∘90^{\circ}, while an Acute Angle is less than 90∘90^{\circ} and an Obtuse Angle is between 90∘90^{\circ} and 180∘180^{\circ}.

A right angle showing the 90 degree square symbol.
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A Straight Angle is formed when the arms of the angle lie in opposite directions, creating a straight line of 180∘180^{\circ}.

A straight angle showing a 180 degree semi-circle.
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A Reflex Angle is larger than a straight angle but smaller than a full rotation (180∘<Reflex Angle<360∘180^{\circ} < \text{Reflex Angle} < 360^{\circ}).

📐Formulae

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

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

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

Straight Angle=180∘\text{Straight Angle} = 180^{\circ}

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

Complete Angle=360∘\text{Complete Angle} = 360^{\circ}

💡Examples

Problem 1:

Identify the type of angle for the following measures: (i) 72∘72^{\circ}, (ii) 180∘180^{\circ}, (iii) 215∘215^{\circ}.

Solution:

(i) Acute Angle, (ii) Straight Angle, (iii) Reflex Angle.

Explanation:

Since 72∘72^{\circ} is less than 90∘90^{\circ}, it is acute. 180∘180^{\circ} is exactly a straight line. 215∘215^{\circ} is greater than 180∘180^{\circ} but less than 360∘360^{\circ}, making it a reflex angle.

Problem 2:

At what angle do the hands of a clock stand at 33 o'clock?

Solution:

90∘90^{\circ}

Explanation:

At 33 o'clock, the minute hand is at 1212 and the hour hand is at 33. This covers one-fourth of the circle. Since a full rotation is 360∘360^{\circ}, 14×360∘=90∘\frac{1}{4} \times 360^{\circ} = 90^{\circ}.

Problem 3:

If an angle is double the size of a right angle, what is its measure and what is it called?

Solution:

2×90∘=180∘2 \times 90^{\circ} = 180^{\circ}. It is a Straight Angle.

Explanation:

A right angle is 90∘90^{\circ}. Doubling it gives 180∘180^{\circ}, which is the definition of a straight angle.

Problem 4:

Identify and name the type of angle shown in the diagram with a measure of 135∘135^{\circ}.

An obtuse angle of 135 degrees.

Solution:

135∘135^{\circ} is an Obtuse Angle.

Explanation:

Since the angle measure is greater than 90∘90^{\circ} but less than 180∘180^{\circ}, it falls under the category of an obtuse angle.

Problem 5:

If the hour hand of a clock moves from 1212 to 99 in a clockwise direction, what is the measure of the angle formed and what type of angle is it?

Clock showing the movement from 12 to 9 creating a 270 degree angle.

Solution:

The angle formed is 270∘270^{\circ}, which is a Reflex Angle.

Explanation:

One full rotation is 360∘360^{\circ}. The clock is divided into 1212 sectors, each being 30∘30^{\circ}. Moving from 1212 to 99 clockwise covers 99 sectors. 9×30∘=270∘9 \times 30^{\circ} = 270^{\circ}. Since 270∘>180∘270^{\circ} > 180^{\circ}, it is a reflex angle.