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Geometry - Measuring and drawing angles

Grade 6Cambridge (IGCSE)

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

🔑Concepts

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An acute angle is any angle that measures greater than 0∘0^\circ and less than 90∘90^\circ.

Diagram showing an acute angle of 45 degrees.
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A right angle measures exactly 90∘90^\circ. It is often marked with a small square symbol in the corner.

Diagram of a 90 degree right angle.
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An obtuse angle measures greater than 90∘90^\circ but less than 180∘180^\circ.

Diagram of an obtuse angle measuring 143 degrees.
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Angles on a straight line always sum to 180∘180^\circ. This is also called a straight angle.

Diagram of a straight line showing a 180 degree angle.

📐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

Reflex Angle=360∘−Interior Angle\text{Reflex Angle} = 360^\circ - \text{Interior Angle}

💡Examples

Problem 1:

Find the missing angle 'x' on a straight line if the other angle is 125°.

Solution:

x=180∘−125∘=55∘x = 180^\circ - 125^\circ = 55^\circ

Explanation:

Since angles on a straight line always sum to 180°, we subtract the known angle from 180° to find the unknown.

Problem 2:

Calculate the reflex angle if the interior (smaller) angle measures 45°.

Solution:

360∘−45∘=315∘360^\circ - 45^\circ = 315^\circ

Explanation:

A full turn is 360°. To find the reflex part, we subtract the acute interior angle from the total 360°.

Problem 3:

Identify the type of angle for the following measurements: 92°, 180°, and 210°.

Solution:

92°: Obtuse; 180°: Straight; 210°: Reflex.

Explanation:

92° is greater than 90° but less than 180° (Obtuse). 180° is a flat line (Straight). 210° is greater than 180° but less than 360° (Reflex).

Problem 4:

Calculate the missing angle aa in the diagram, given that the angles are around a point.

Diagram showing three angles meeting at a point: 90 degrees, 150 degrees, and unknown angle a.

Solution:

a=360∘−(150∘+90∘)a = 360^\circ - (150^\circ + 90^\circ) a=360∘−240∘a = 360^\circ - 240^\circ a=120∘a = 120^\circ

Explanation:

The sum of all angles meeting at a single point is 360∘360^\circ. By subtracting the known angles (150∘150^\circ and 90∘90^\circ) from 360∘360^\circ, we find the value of aa.

Problem 5:

Identify the value of angle yy on the straight line shown.

Diagram showing a straight line split into two angles: y and 55 degrees.

Solution:

y=180∘−55∘y = 180^\circ - 55^\circ y=125∘y = 125^\circ

Explanation:

Angles on a straight line add up to 180∘180^\circ. To find yy, subtract the given angle 55∘55^\circ from 180∘180^\circ.

Measuring and drawing angles Grade 6 Notes & Examples