Answer:
Step-by-step explanation:
n=14
(n-2)180*=(14-2)180*
=(12)180*
=2,160*
the sum of the interior angle is 2,160*
2,180 + X =2,160*
X = 142*
the fourteenth angle measures 142*
The measurement of the fourteenth angle of the 14-gon is 146°
From the question,
We are to determine the measure of the fourteenth angle of a 14-gon
First, we will determine the sum of angles in the polygon.
The sum of angles in a polygon is given by the formula
S = (n-2)180°
Where n is the number of sides
∴ The sum of angles in a 14-gon = (14-2)180°
The sum of angles in a 14-gon = 12 × 180°
The sum of angles in a 14-gon = 2160°
From the given information, we have that
The measures of 13 angles of the 14-gon add up to 2014°.
Let the fourteenth angle be x
Then, we can write that
2014° + x = 2160°
∴ x = 2160° - 2014°
x = 146°
Hence, the measurement of the fourteenth angle of the 14-gon is 146°
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