How do I find the interior angles of an irregular polygon WITH one external angle? I have an image as an example, but Jiskha won't allow internet addresses. What do I do?

if the polygon is irregular, no joy.

All you know is that at each vertex the sum of the interior/exterior angles is 180°

This didn't help, and I still am confused.

Sorry for being negative if I am being :)

To find the interior angles of an irregular polygon with one external angle, you can follow these steps:

1. Count the number of sides (edges) of the polygon and label them from 1 to n, starting from any side.

2. Identify the external angle, which is the angle formed between the extended line of one side and the next side.

3. Measure the value of the external angle using a protractor or any other measuring tool.

4. Calculate the interior angle by subtracting the value of the external angle from 180 degrees. Since the sum of the interior angles of any polygon is always equal to 180 degrees times (n - 2), where n is the number of sides, you can use this formula to find the total sum of the interior angles.

For example, if you have a polygon with 6 sides, the formula would be: Sum of interior angles = (6 - 2) * 180 = 4 * 180 = 720 degrees.

Then, if you're given the measure of the external angle, let's say it is 45 degrees, you can find the interior angle of any side by subtracting the given external angle from 180 degrees: Interior angle = 180 degrees - 45 degrees = 135 degrees.

Repeat this process for each side to find the interior angles of the remaining sides.

As for sharing the image example, since Jiskha doesn't allow internet addresses, you have a few alternatives:

1. You can describe the polygon and its external angle in words, providing as much detail as possible.

2. You can upload the image to an image hosting platform (such as Imgur), which would provide you with a direct link to the image. Then, you can describe the link without providing the actual address (e.g., "Replace the '[DOT]' with a period, and '[SLASH]' with a forward slash, and you will have the link to the image").

3. You can draw the polygon using any drawing or geometry software or application, and then provide a detailed description of the polygon and its external angle based on the drawing.

Remember, the more information you provide, the easier it will be to assist you in finding the interior angles of the irregular polygon.