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Geometry - Types of Angles

Grade 4ICSE

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

🔑Concepts

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An angle is formed when two rays meet at a common endpoint called the vertex. The rays are known as the arms of the angle.

An angle showing a vertex and two arms.
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An Acute Angle measures more than 0∘0^{\circ} but less than 90∘90^{\circ}. It looks like a partially open pair of scissors.

Acute angle of 45 degrees.
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A Right Angle measures exactly 90∘90^{\circ}. It forms an 'L' shape and is often marked with a small square at the vertex.

Right angle of 90 degrees.
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An Obtuse Angle measures more than 90∘90^{\circ} but less than 180∘180^{\circ}. It is wider than a right angle.

Obtuse angle of 135 degrees.
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A Straight Angle measures exactly 180∘180^{\circ}. It appears as a straight line.

Straight angle of 180 degrees.

📐Formulae

textAcuteAngle:0circ<textMeasure<90circ\\text{Acute Angle}: 0^{\\circ} < \\text{Measure} < 90^{\\circ}

textRightAngle:textMeasure=90circ\\text{Right Angle}: \\text{Measure} = 90^{\\circ}

textObtuseAngle:90circ<textMeasure<180circ\\text{Obtuse Angle}: 90^{\\circ} < \\text{Measure} < 180^{\\circ}

textStraightAngle:textMeasure=180circ\\text{Straight Angle}: \\text{Measure} = 180^{\\circ}

textCompleteAngle:textMeasure=360circ\\text{Complete Angle}: \\text{Measure} = 360^{\\circ}

💡Examples

Problem 1:

Classify the following angles based on their degree measures: (a) 45circ45^{\\circ}, (b) 165circ165^{\\circ}, (c) 90circ90^{\\circ}.

Solution:

Step 1: Check 45circ45^{\\circ}. Since 45circ45^{\\circ} is greater than 0circ0^{\\circ} and less than 90circ90^{\\circ}, it is an Acute Angle. Step 2: Check 165circ165^{\\circ}. Since 165circ165^{\\circ} is greater than 90circ90^{\\circ} and less than 180circ180^{\\circ}, it is an Obtuse Angle. Step 3: Check 90circ90^{\\circ}. Since it is exactly 90circ90^{\\circ}, it is a Right Angle.

Explanation:

To identify an angle, compare the given measure against the standard benchmarks: 90circ90^{\\circ} (Right) and 180circ180^{\\circ} (Straight).

Problem 2:

What type of angle is formed if you add 40circ40^{\\circ} to a 50circ50^{\\circ} angle? Show the calculation.

Solution:

Step 1: Find the total measure by adding the two angles: 50circ+40circ=90circ50^{\\circ} + 40^{\\circ} = 90^{\\circ}. Step 2: Identify the type of angle that measures exactly 90circ90^{\\circ}. The result is a Right Angle.

Explanation:

First, calculate the sum of the angles. Then, use the definition of a right angle (90circ90^{\\circ}) to classify the result.

Problem 3:

Look at the clock face where the hour hand is at 12 and the minute hand is at 4. What is the type of angle formed between the two hands if the angle measure is 120∘120^{\circ}?

Clock showing 4 o'clock forming an obtuse angle.

Solution:

Angle measure=120∘\text{Angle measure} = 120^{\circ} Since 90∘<120∘<180∘90^{\circ} < 120^{\circ} < 180^{\circ}, the angle is an obtuse angle.

Explanation:

Any angle that measures more than 90∘90^{\circ} but less than 180∘180^{\circ} is classified as an obtuse angle.

Problem 4:

A carpenter cuts a piece of wood at an angle of 30∘30^{\circ}. Identify the type of angle and show it in relation to a 90∘90^{\circ} corner.

An acute angle of 30 degrees shown inside a rectangular frame.

Solution:

Angle=30∘\text{Angle} = 30^{\circ} Since 0∘<30∘<90∘0^{\circ} < 30^{\circ} < 90^{\circ}, it is an acute angle.

Explanation:

Angles smaller than a right angle (90∘90^{\circ}) are called acute angles.