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Geometry - Classifying angles (acute, obtuse, right, reflex)

Grade 4Cambridge (IGCSE)

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

🔑Concepts

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An acute angle is a sharp angle that measures more than 0∘0^{\circ} and less than 90∘90^{\circ}.

Diagram of an acute angle showing a sharp opening less than 90 degrees.
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A right angle measures exactly 90∘90^{\circ}. It is often indicated by a small square at the vertex and looks like the corner of a square or the letter 'L'.

Diagram of a right angle forming a perfect L-shape with a square symbol.
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An obtuse angle is wider than a right angle but smaller than a straight line. Its measure is between 90∘90^{\circ} and 180∘180^{\circ}.

Diagram of an obtuse angle showing a wide opening between 90 and 180 degrees.
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A reflex angle is an angle that is greater than 180∘180^{\circ} but less than 360∘360^{\circ}. It represents the 'outer' part of an angle.

Diagram of a reflex angle showing the large outer turn greater than a straight line.

📐Formulae

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

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

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

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

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

Full Turn:x=360∘\text{Full Turn}: x = 360^{\circ}

💡Examples

Problem 1:

An angle measures 45∘45^{\circ}. Classify this angle.

Solution:

Acute Angle

Explanation:

Because 45∘45^{\circ} is greater than 0∘0^{\circ} but less than 90∘90^{\circ}, it is classified as an acute angle.

Problem 2:

What type of angle is 135∘135^{\circ}?

Solution:

Obtuse Angle

Explanation:

135∘135^{\circ} is larger than a right angle (90∘90^{\circ}) but smaller than a straight line (180∘180^{\circ}).

Problem 3:

Identify the type of angle for 210∘210^{\circ}.

Solution:

Reflex Angle

Explanation:

Any angle that is greater than 180∘180^{\circ} but less than 360∘360^{\circ} is called a reflex angle.

Problem 4:

If two lines meet to form a perfect 'L' shape, what is the angle and its name?

Solution:

90∘90^{\circ}, Right Angle

Explanation:

A perfect 'L' shape represents a quarter-turn, which is exactly 90∘90^{\circ} and is known as a right angle.

Problem 5:

Determine the classification of the angle aa shown in the diagram, which measures 315∘315^{\circ}.

A diagram showing an angle of 315 degrees, which is a reflex angle.

Solution:

a=315∘  ⟹  Reflex Anglea = 315^{\circ} \implies \text{Reflex Angle}

Explanation:

Since the angle aa is greater than 180∘180^{\circ} but less than 360∘360^{\circ}, it is classified as a reflex angle.

Problem 6:

Identify the type of angle bb that measures 12∘12^{\circ} as shown in the geometry figure.

A diagram showing a very small angle of 12 degrees, classified as acute.

Solution:

b=12∘  ⟹  Acute Angleb = 12^{\circ} \implies \text{Acute Angle}

Explanation:

An angle that measures less than 90∘90^{\circ} is called an acute angle. Because 12∘<90∘12^{\circ} < 90^{\circ}, this is acute.