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Geometry - Measuring and drawing angles with a protractor

Grade 5Cambridge (IGCSE)

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

🔑Concepts

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The vertex of the angle must be aligned exactly with the center point of the protractor, and the base line of the angle must align with the 0∘0^{\circ} line on the scale.

Diagram showing the correct alignment of a protractor center point on the vertex and the base line on zero.
•

Identify the type of angle before measuring: Acute angles are less than 90∘90^{\circ}, obtuse angles are between 90∘90^{\circ} and 180∘180^{\circ}, and reflex angles are greater than 180∘180^{\circ}.

Comparison of acute and obtuse angles.
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Protractors usually have two scales (inner and outer). Use the scale that starts at 0∘0^{\circ} on the arm of the angle you are measuring from.

•

To draw an angle, first draw a straight line (the base arm), place the protractor center on the start point, mark the required degree, and join the points.

📐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}.

Problem 4:

Use a protractor to measure the angle ABCABC shown in the diagram.

An obtuse angle ABC to be measured.

Solution:

The angle measures 120∘120^{\circ}.

Explanation:

  1. Place the center of the protractor on vertex BB.
  2. Align the base line of the protractor with the line BCBC (pointing to 0∘0^{\circ} on the inner scale).
  3. Follow the inner scale around to where the line BABA crosses it, which is at 120∘120^{\circ}.

Problem 5:

Draw an acute angle of 45∘45^{\circ} starting from point PP.

A 45-degree angle labeled PQR.

Solution:

An angle of 45∘45^{\circ} is created between the horizontal base and the newly drawn arm.

Explanation:

  1. Draw a horizontal line PQPQ.
  2. Place the protractor center on PP.
  3. Find 45∘45^{\circ} on the scale and mark a point RR.
  4. Connect PP to RR with a straight line.