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Geometry - Right angles and turns

Grade 3Cambridge (IGCSE)

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

🔑Concepts

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A right angle is the corner of a square. It represents a 90∘90^{\circ} turn or one quarter turn.

A diagram showing a 90 degree right angle with a square symbol at the vertex.
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A half turn is equal to two right angles and forms a straight line (180∘180^{\circ}).

A straight line showing a 180 degree arc representing a half turn.
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A full turn is equal to four right angles, returning to the original position (360∘360^{\circ}).

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Turns can be clockwise (following the direction of clock hands) or anti-clockwise (the opposite direction).

A circle with an arrow indicating clockwise direction.

📐Formulae

1 quarter turn=1 right angle=90∘1 \text{ quarter turn} = 1 \text{ right angle} = 90^\circ

1 half turn=2 right angles=180∘1 \text{ half turn} = 2 \text{ right angles} = 180^\circ

1 full turn=4 right angles=360∘1 \text{ full turn} = 4 \text{ right angles} = 360^\circ

💡Examples

Problem 1:

How many right angles are there inside a standard rectangle?

Solution:

4 right angles

Explanation:

A rectangle has four corners, and each corner is a perfect 'L' shape or a square corner, which measures 90∘90^\circ.

Problem 2:

If Sarah is facing North and makes a half turn, which direction is she facing now?

Solution:

South

Explanation:

A half turn is equal to two right angles. Moving two right angles from North (whether clockwise or anti-clockwise) points you in the opposite direction, which is South.

Problem 3:

Identify if the angle formed by the hands of a clock at 1:00 is 'greater than', 'less than', or 'equal to' a right angle.

Solution:

Less than a right angle

Explanation:

At 3:00, the hands form a perfect right angle (90∘90^\circ). At 1:00, the gap between the hands is much smaller than the 'L' shape of a right angle.

Problem 4:

A robot makes 3 quarter turns clockwise. How many right angles has it turned through?

Solution:

3 right angles

Explanation:

Since each quarter turn is equal to 1 right angle, 3 quarter turns equals 3×1=33 \times 1 = 3 right angles.

Problem 5:

Determine the type of turn required to move the arrow from pointing at the letter A to pointing at the letter B in the diagram.

An L-shape showing points A and B at 90 degrees to each other.

Solution:

One quarter turn clockwise (or 1 right angle).

Explanation:

The arrow moves from North (A) to East (B). This is a 90∘90^{\circ} movement in the direction of clock hands, which is one quarter turn clockwise.

Problem 6:

If a dial starts at 0 and moves through 3 right angles anti-clockwise, where will it point?

A circle dial showing a 270 degree anti-clockwise turn.

Solution:

It will point to the '9' position (West).

Explanation:

Each right angle is a quarter turn. Three right angles anti-clockwise is a 34\frac{3}{4} turn. Starting from the top (12/0), one turn lands at 9, two turns at 6, and three turns anti-clockwise lands at the 3 o'clock position if moving clockwise, but because we are moving anti-clockwise: 1st turn = 9, 2nd turn = 6, 3rd turn = 3. Wait, the calculation is: 270∘270^{\circ} anti-clockwise from North is East.