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

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

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

Therefore, each exterior angle measures 45°.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1