The diagram shows a regular decagon. Find the size of one exterior angle of this decagon and write down its order of rotational symmetry.
Question 1 Report
The diagram shows a regular decagon.
Find the size of one exterior angle of this decagon and write down its order of rotational symmetry.
Answer Details
A decagon has \( 10 \) sides. In a regular polygon the exterior angles are all equal and add up to \( 360^\circ \), so each one is
\[ 360 \div 10 = 36^\circ \] [B1]The order of rotational symmetry is the number of positions in one full turn in which the shape looks exactly the same as it started. Turning a regular decagon by one exterior angle, \( 36^\circ \), moves each vertex onto the next and leaves the shape looking identical, and \( 360 \div 36 = 10 \) such turns fit into a full revolution. The order of rotational symmetry is therefore \( 10 \). [B1]
This is a general pattern worth remembering: a regular \( n \)-sided polygon has \( n \) lines of symmetry and rotational symmetry of order \( n \), and its exterior angle is \( \frac{360}{n} \) degrees. Do not confuse the exterior angle of \( 36^\circ \) with the interior angle, which here is \( 180 - 36 = 144^\circ \).
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