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Shapes and Angles - Right, Acute, and Obtuse Angles

Grade 5CBSE

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

🔑Concepts

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An angle is formed when two lines meet at a common point called the vertex. We measure angles in degrees using the symbol ∘^{\circ}.

Diagram showing an angle with labeled vertex and arms.
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A Right Angle looks like the corner of a square or the letter 'L'. It measures exactly 90∘90^{\circ}.

A right angle measuring 90 degrees.
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An Acute Angle is 'smaller' than a right angle. Its measure is always more than 0∘0^{\circ} but less than 90∘90^{\circ}.

An acute angle which is less than 90 degrees.
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An Obtuse Angle is 'wider' than a right angle. Its measure is more than 90∘90^{\circ} but less than 180∘180^{\circ}.

An obtuse angle which is greater than 90 degrees.

📐Formulae

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

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

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

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

Sum of angles in a Right Angle=90∘\text{Sum of angles in a Right Angle} = 90^{\circ}

💡Examples

Problem 1:

Identify the type of angle for the following measurements: (a) 35∘35^{\circ}, (b) 145∘145^{\circ}, and (c) 90∘90^{\circ}.

Solution:

Step 1: Compare 35∘35^{\circ} to 90∘90^{\circ}. Since 35∘<90∘35^{\circ} < 90^{\circ}, it is an Acute Angle. Step 2: Compare 145∘145^{\circ} to 90∘90^{\circ} and 180∘180^{\circ}. Since 90∘<145∘<180∘90^{\circ} < 145^{\circ} < 180^{\circ}, it is an Obtuse Angle. Step 3: 90∘90^{\circ} is exactly the measurement of a Right Angle.

Explanation:

To classify angles, we use 90∘90^{\circ} as the primary benchmark. Angles smaller than 90∘90^{\circ} are acute, larger are obtuse, and exactly 90∘90^{\circ} are right.

Problem 2:

If two angles are joined to form a right angle, and one of the angles is 40∘40^{\circ}, what is the measure of the other angle?

Solution:

Step 1: Recall that a Right Angle is exactly 90∘90^{\circ}. Step 2: Set up the equation: 40∘+unknown angle=90∘40^{\circ} + \text{unknown angle} = 90^{\circ}. Step 3: Subtract the known angle from the total: 90∘−40∘=50∘90^{\circ} - 40^{\circ} = 50^{\circ}. The second angle is 50∘50^{\circ}.

Explanation:

Since the combined shape is a right angle, the sum of its parts must equal 90∘90^{\circ}. We use subtraction to find the missing part.

Problem 3:

Look at the hands of the clock shown in the diagram. What type of angle is formed between the hour hand and the minute hand at 2 o'clock?

Clock showing 2 o'clock forming an acute angle.

Solution:

The angle formed is an Acute Angle.

Explanation:

At 2 o'clock, the angle is smaller than a right angle (90∘90^{\circ}). Specifically, since each hour mark represents 30∘30^{\circ}, the angle is 2×30∘=60∘2 \times 30^{\circ} = 60^{\circ}, which is less than 90∘90^{\circ}.

Problem 4:

In the following figure, a large right angle is divided into two parts. If the measure of one part is 30∘30^{\circ}, find the value of the angle marked as xx.

A 90 degree angle split into 30 degrees and x.

Solution:

x=60∘x = 60^{\circ}

Explanation:

The total angle is a right angle, which means its total measure is 90∘90^{\circ}. We can set up the equation: 30∘+x=90∘30^{\circ} + x = 90^{\circ}. Subtracting 30∘30^{\circ} from both sides, we get x=90∘−30∘=60∘x = 90^{\circ} - 30^{\circ} = 60^{\circ}.