Mattea was asked to find the measure of an interior angle of a regular octagon. Mattea’s work is shown below.

Steps
Mattea’s Work
Step 1
(n minus 2) 180 degrees = (9 minus 2) 180 degrees
Step 2
7 (180 degrees) = 1260 degrees
Step 3
1260 degrees divided by 8 = 157.5 degrees

Where, if at all, did Mattea first make a mistake finding the measure of an interior angle?
step 1
step 2
step 3
Mattea did not make a mistake.

141 3/7 degrees, Mattea did not make a mistake.

Step-by-step explanation:

Find each of the interior angles of the regular heptagon.  

The formula that gives the interior angle measure for a regular polygon with any number of sides is 180(n-2)/n where n is the number of sides.

So a regular heptagon's interior angle measures: 180(7-2)/7 = 128 4/7.  

Angle A and D would be 128 4/7 degrees.

Step 2: Find angle BAC. We know that a square's interior angle is 90 degrees and a heptagon's is 128 4/7 degrees. We will subtract those from 360 degrees to find angle BAC.

Angle BAC = 360 - (angle A + 90)

                  = 360 - (128 4/7 + 90)

                  = 360 - 218 4/7

                  = 141 3/7 degrees

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