A corner shop has a new sign made in the shape of a regular hexagon. corner shop sign© EAGLE BEACON GLOBAL Work out the sum of the interior angles of a hexa...
Question 1 Report
A corner shop has a new sign made in the shape of a regular hexagon.
- Work out the sum of the interior angles of a hexagon. (2)
- Hence write down the size of one interior angle of the sign. (1)
Answer Details
This question uses the formula for the sum of the interior angles of a polygon.
(a) For any polygon with \(n\) sides, the interior angles sum to \((n-2) \times 180^\circ\). For a hexagon, \(n = 6\), so the sum is \((6-2) \times 180\). [1 mark]
This gives \(720^\circ\). [1 mark]
(b) Since a regular hexagon has six equal interior angles, one interior angle is the total shared equally: \(720 \div 6 = 120^\circ\). [1 mark]
The formula \((n-2) \times 180^\circ\) comes from splitting any polygon into \((n-2)\) triangles, each contributing \(180^\circ\) to the total.
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