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Geometry - Measuring and drawing angles with a protractor

Grade 4IGCSE

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

🔑Concepts

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Angle Definition: An angle is formed when two rays or line segments meet at a common point called the vertex.

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

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Alignment: To measure, the center point (crosshair) of the protractor must be placed exactly on the vertex of the angle.

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Zero Line: One arm of the angle must line up perfectly with the 0° line on the protractor.

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Choosing the Scale: If the zero you aligned with is on the inner scale, read the inner numbers. If it is on the outer scale, read the outer numbers.

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Classifying Angles: Before measuring, estimate if the angle is Acute (<90°), Right (90°), or Obtuse (>90° but <180°) to ensure your reading makes sense.

📐Formulae

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

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

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

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

💡Examples

Problem 1:

You are measuring an angle. You place the center of the protractor on the vertex and align the right arm of the angle with the 0° mark on the inner scale. The other arm points between 50 and 60, specifically at the 55 mark on the inner scale. What is the measurement?

Solution:

55°

Explanation:

Because the baseline arm aligned with the 0° on the inner scale, we must follow the inner scale to find the measurement. The arm points to 55°, which is an acute angle.

Problem 2:

Describe the steps to draw an angle of 130°.

Solution:

  1. Draw a straight horizontal line. 2. Mark a point (vertex) at the left end. 3. Place the protractor center on the vertex and the 0° line on the ray. 4. Using the scale starting at 0°, find 130° and make a dot. 5. Remove the protractor and join the vertex to the dot.

Explanation:

Since 130° is greater than 90°, the resulting angle should be obtuse (wider than a square corner).

Problem 3:

If an angle is measured using the wrong scale and the student reads 150°, but the angle is clearly acute, what is the correct measurement?

Solution:

30°

Explanation:

Standard protractors have scales that add up to 180° at any given point (180−150=30180 - 150 = 30). If the student read 150° (obtuse) but the angle is acute, they likely looked at the wrong scale. The corresponding measurement on the opposite scale is 30°.