What is the sum of the angles in a star?

We know the sum of the internal angles in a triangle is always 180°. We also know that the sum of the internal angles in a quadrilateral is always 360°. What about the sum of the angles in a five-pointed star?

For this investigation, create several different five-pointed stars. Then measure the internal angles of the five points. Record your measurements in a table. Use words, numbers, and pictures to clearly explain your findings.

Examples of stars:

Use this applet to help with your investigation.

Directions:

1. Create a 5-pointed star and then use the checkbox to "pin" the vertices down.
2. Use the protractor to measure the five internal angles.
3. Find the sum of the angles.
4. Make a new star. Do you get similar results?

Angles in a Star Grading Rubric

 Category 1 2 3 4 Stars Stars are missing from the write-up. Stars have not been labeled with angle letters and/or degree measurements. Stars are shown with their angles clearly labeled with the letter and the degrees measurement, but there are not enough stars included. Several stars are shown with their angles clearly labeled with a letter and the degrees measurement. Use of protractor There are several protractor mistakes. Most angles have been measured correctly. Nearly every angle has been measured correctly. All angles have been accurately measured with a protractor. Table Table is messy or is missing important information. Table is messy and hard to read, but has all information. Table includes all necessary information, but is not particularly neat. Table is neatly drawn with a title for each column. Table includes all necessary information. Conclusion statement Conclusion is wrong and not in sentence form. The conclusion is incorrect, but at least it was written in sentence form. The conclusion is correct, but has not been written in sentence form. The conclusion is written in sentence form and the conclusion is correct. Neatness Paper is wrinkled. Writing is messy. Stars drawn poorly. Everything is easy to read, but the overall look is not neat and organized. All writing, mathematics, and stars are neat, easy to read. All writing, mathematics, and stars are neat, easy to read, and include color.