对于一个正 n 边形，其一个内角与一个外角的大小之比为 7 : 2。

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完整解法

1. Use the ratio of interior angle to exterior angle to find the interior angle.

Interior angle : exterior angle $= 7 : 2$

Total parts $= 7+2=9$ .

Since an interior angle and its exterior angle add up to $180^\circ$ ,

$\text{interior angle}=\frac{7}{9}\times 180^\circ=140^\circ.$

答案

$140^\circ$

1. Find the exterior angle using the interior angle from part (a).

From part (a), the interior angle is $140^\circ$ .

Since the interior angle and exterior angle of a polygon add to $180^\circ$ ,

$\text{exterior angle} = 180^\circ - 140^\circ = 40^\circ$ .

2. Use the exterior angle of a regular polygon to find the number of sides.

For a regular polygon,

$\text{exterior angle} = \dfrac{360^\circ}{n}$ .

$\dfrac{360}{n} = 40$

$n = \dfrac{360}{40} = 9$ .

答案

$n = 9$

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