The diagram shows a regular polygon with 6 lines of symmetry. Calculate the size of each interior angle of this polygon.
Question 1 Report
The diagram shows a regular polygon with 6 lines of symmetry.
Calculate the size of each interior angle of this polygon.
Answer Details
For a regular polygon the number of lines of symmetry equals the number of sides, so 6 lines of symmetry means this is a regular hexagon.
There are two standard routes to one interior angle, and either earns the method mark.
- Exterior angle first: the exterior angles sum to \(360^\circ\), so each is \(360\div 6 = 60^\circ\), and the interior angle is its supplement, \(180-360\div 6\).
- Angle sum first: the interior angles of an \(n\)-sided polygon sum to \((n-2)\times 180^\circ\), so here \((6-2)\times 180 = 720^\circ\), shared equally as \((6-2)\times 180\div 6\).
\(180-360\div 6\) or \((6-2)\times 180\div 6\) [M1]
\[ = 120^\circ \] [A1]Each interior angle is \(120^\circ\). A useful check is that \(6\times 120 = 720\), which matches the angle sum, and that \(120^\circ\) is obtuse, as it must be for any regular polygon with more than four sides.
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