Open Middle®
Directions: The measures of the angles of a convex polygon form an arithmetic sequence. The smallest angle has a measurement of 129 degrees. The largest angle has a measurement of 159 degrees. Find the number of sides in this polygon.
Hint
What are the equations that relate the missing information to the given information?
What formulas do you know that involve arithmetic sequences?
What formulas do you know that involve angles of a polygon?
Answer
10 sides
Source: Ricardo Navarro
I loved this one
Does anyone have a solution for this that they can share?
Because you know the first and last terms, you have values to plug into the arithmetic sequence formula, except for the difference between terms, and which term count produces the final value of the sequence. You can plug in different values for the term count (the answer the question seeks), and solve each to reveal the difference between terms. Eventually you will plug in a term count where the difference from term to term produces angles in the sequence for which the external angles for each term totals 360 degrees. (It turns out to be a fractional difference between terms rather than an integer that produces the noted answer of 10 terms.)
This was a good opportunity to teach how to use Google Sheets formulas to do the repetitive calculation for each possible term count, to see if the external angles summed to 360.