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Measurement - Measuring and Drawing Angles

Grade 5IB

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

🔑Concepts

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An angle is formed when two rays meet at a common endpoint called the vertex. We measure the amount of turn between these two rays in degrees (∘^\circ) using a protractor.

Diagram showing an angle formed by two rays meeting at a vertex.
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Angles are classified based on their size: Acute angles are less than 90∘90^\circ, Right angles are exactly 90∘90^\circ, Obtuse angles are between 90∘90^\circ and 180∘180^\circ, and Reflex angles are greater than 180∘180^\circ but less than 360∘360^\circ.

Illustration of a 90 degree right angle.
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To measure an angle, place the center of the protractor on the vertex and align the zero line with one ray. Read the scale where the second ray crosses the protractor.

Protractor guide showing the alignment of the base line and center point.
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A full turn or a circle measures exactly 360∘360^\circ. This represents the sum of angles around a single point.

📐Formulae

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

Sum of angles around a point=360∘\text{Sum of angles around a point} = 360^\circ

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

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

Missing Angle x=180∘−known angle (on a straight line)\text{Missing Angle } x = 180^\circ - \text{known angle (on a straight line)}

💡Examples

Problem 1:

Calculate the missing angle xx on a straight line if the adjacent angle is 115∘115^\circ.

Solution:

x+115∘=180∘x + 115^\circ = 180^\circ x=180∘−115∘x = 180^\circ - 115^\circ x=65∘x = 65^\circ

Explanation:

Since angles on a straight line must sum to 180∘180^\circ, we subtract the given angle from 180∘180^\circ to find the unknown value.

Problem 2:

An angle measures 210∘210^\circ. Classify this angle and explain why.

Solution:

The angle is a Reflex Angle.

Explanation:

By definition, any angle that is greater than 180∘180^\circ but less than 360∘360^\circ is classified as a reflex angle. Since 180∘<210∘<360∘180^\circ < 210^\circ < 360^\circ, it fits this category.

Problem 3:

Identify the type of angle shown in the diagram and measure its size if one ray points to 0∘0^\circ and the other points to 135∘135^\circ on the protractor.

An obtuse angle measuring 135 degrees.

Solution:

The angle measures 135∘135^\circ. Since 135∘135^\circ is greater than 90∘90^\circ but less than 180∘180^\circ, it is an obtuse angle.

Explanation:

We compare the measured angle to the benchmark of 90∘90^\circ. Because it is 'wider' than a square corner but 'narrower' than a straight line, it fits the definition of an obtuse angle.

Problem 4:

Find the missing angle aa if it combines with a 45∘45^\circ angle to form a perfect right angle.

A right angle split into two 45 degree angles.

Solution:

a=90∘−45∘=45∘a = 90^\circ - 45^\circ = 45^\circ

Explanation:

A right angle is exactly 90∘90^\circ. If one part is 45∘45^\circ, we subtract that from 90∘90^\circ to find the remaining part.