Question

The center of the stained glass window is in the shape of a regular polygon.what is the measure of each exterior angle? ∘

Answer 1

A regular polygon is a polygon which has sides of equal length and angles between them also equal. The number of sides and angle measurements depend on the shape of the regular polygon. If the shape of the regular polygon is a  square, its interior angle is equal to 90° and the exterior angle of 90°. If the shape is a regular hexagon which has 6 sides. The exterior angles add up to 360 divided by 6 angles= 60 °while the interior angle is (180-6)=120°.

Please note that the interior angle and its corresponding exterior angle always add up to 180° (for a regular octagon, the exterior angle is 360/8=45 while the interior angle is 180 - 45 = 135°.

Answer 2

Answer:

Each exterior angle measures 45°.

Step-by-step explanation:

First of all, we have to know that a stained glass window has 8 sides. So, it's a regular polygon with 8 sides.

Now, the sum of all interior angles of any regular polygon is expressed as

$S=(n-2)180$

However, the problem is asking only about exterior angles.

We know by definition that a polygon exterior angles sum 360°, and in this case, the polygon has 8 equal exterior angels. So, each of them would measure

$\frac{360}{8}=45\°$

Therefore, each exterior angle measures 45°.