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Geometry - Right angles and turns

Grade 3IGCSE

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

🔑Concepts

A right angle is a 'square corner' angle, measuring exactly 9090^\circ.

A quarter turn is equivalent to one right angle.

A half turn is equivalent to two right angles (180180^\circ).

A three-quarter turn is equivalent to three right angles (270270^\circ).

A full turn (whole turn) is equivalent to four right angles (360360^\circ), returning to the original position.

Clockwise means moving in the same direction as the hands of a clock.

Anti-clockwise means moving in the opposite direction to the hands of a clock.

Angles can be compared to a right angle: they can be smaller than (acute) or larger than (obtuse) a right angle.

📐Formulae

1 quarter turn=1 right angle=901 \text{ quarter turn} = 1 \text{ right angle} = 90^\circ

1 half turn=2 right angles=1801 \text{ half turn} = 2 \text{ right angles} = 180^\circ

1 full turn=4 right angles=3601 \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 9090^\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 (9090^\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.