Geometry - Measuring and drawing angles

Grade 6IGCSE

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

🔑Concepts

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

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Types of Angles: Acute (less than 90°), Right (exactly 90°), Obtuse (between 90° and 180°), Straight (exactly 180°), Reflex (between 180° and 360°), and Full Turn (360°).

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Measuring with a Protractor: Place the crosshair on the vertex and the zero line along one arm of the angle. Read the scale that starts at zero on that arm.

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Drawing Angles: Use a ruler to draw the first arm, place the protractor's center on the vertex, mark the required degree, and join the mark to the vertex.

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Reflex Angles: To measure a reflex angle, measure the smaller interior angle and subtract it from 360°.

📐Formulae

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

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

\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^\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^\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).