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

Grade 4IGCSE

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

🔑Concepts

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An angle is the measure of turn between two lines that meet at a point called a vertex.

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Angles are measured in degrees (°).

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A right angle is often marked with a small square instead of an arc.

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Acute angles are smaller than a right angle (less than 90°).

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Obtuse angles are larger than a right angle but smaller than a straight line (between 90° and 180°).

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Reflex angles are larger than a straight line (between 180° and 360°).

📐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.