Answer: x = 7
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Explanation:
We have n = 8 sides for this octagon.
This means the interior angles sum to 180(n-2) = 180(8-2) = 180*6 = 1080 degrees.
The tickmarks tell us that each side is the same length, so we have a regular octagon. This means that all 8 angles are the same measure. Let's say each angle is y degrees.
1 angle = y degrees
8 angles = 8y degrees
Solving 8y = 1080 leads to y = 1080/8 = 135
Each angle of this regular octagon is 135 degrees.
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Now set 16x+23 equal to 135 and solve for x
16x+23 = 135
16x+23-23 = 135-23
16x = 112
16x/16 = 112/16
x = 7
