图中展示了一个正五边形和一个正八边形。计算 $x$ 的值。 答案 x = ...

1. Find the interior angle of the regular pentagon.

For a regular pentagon,
$\text{interior angle}=\frac{(5-2)\times180^\circ}{5}=108^\circ.$

2. Find the interior angle of the regular octagon.

For a regular octagon,
$\text{interior angle}=\frac{(8-2)\times180^\circ}{8}=135^\circ.$

3. Use angles at a point to calculate $x$.

At the top endpoint of the common side, the angles around the point are $108^\circ$, $135^\circ$ and $x^\circ$.

$x=360^\circ-108^\circ-135^\circ=117^\circ.$

However, since $x$ is the angle between the two non-common adjacent sides outside the two polygons, it is the smaller angle:
$x=180^\circ-117^\circ=63^\circ.$