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Geometry - Measuring and drawing angles with a protractor

Grade 5IGCSE

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

🔑Concepts

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Understanding Angles: An angle is formed when two rays meet at a common endpoint called the vertex.

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The Protractor: A tool used to measure angles in degrees (°). It has two scales: an inner scale (0 to 180) and an outer scale (180 to 0).

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Types of Angles: Acute (< 90°), Right (90°), Obtuse (> 90° and < 180°), Straight (180°), and Reflex (> 180°).

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Measuring Angles: Align the center mark of the protractor with the vertex and the zero line with one side (arm) of the angle. Read the scale that starts at 0 from that side.

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Drawing Angles: Draw a straight line, place the protractor's center on one end, mark the required degree, and join the mark to the vertex.

📐Formulae

Sum of angles on a straight line=180∘\text{Sum of angles on a straight line} = 180^{\circ}

Sum of angles at a point (full turn)=360∘\text{Sum of angles at a point (full turn)} = 360^{\circ}

Sum of angles in a triangle=180∘\text{Sum of angles in a triangle} = 180^{\circ}

💡Examples

Problem 1:

Measure an angle where one arm points to the right-hand '0' and the other arm points towards '75' on the inner scale.

Solution:

75∘75^{\circ}

Explanation:

Since the baseline of the angle is aligned with the right-hand zero, we follow the inner scale starting from zero up to the line, which reaches 75.

Problem 2:

Identify the type of angle that measures 135∘135^{\circ}.

Solution:

Obtuse Angle

Explanation:

An angle is classified as obtuse if it is greater than 90∘90^{\circ} but less than 180∘180^{\circ}. Since 135∘135^{\circ} falls in this range, it is obtuse.

Problem 3:

An angle on a straight line is divided into two parts. One part is 60∘60^{\circ}. Calculate the missing angle.

Solution:

120∘120^{\circ}

Explanation:

Angles on a straight line add up to 180∘180^{\circ}. Therefore, the missing angle is 180∘−60∘=120∘180^{\circ} - 60^{\circ} = 120^{\circ}.