SOLUTION: Three of the exterior angles of an n-sided polygon are 50°each, two of its iterior angles are 127° and 135°,and the remaining interior angles are 173°each. Find the value of n.

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Question 1163881: Three of the exterior angles of an n-sided polygon are 50°each, two of its iterior angles are 127° and 135°,and the remaining interior angles are 173°each. Find the value of n.
Found 3 solutions by Alan3354, Theo, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Three of the exterior angles of an n-sided polygon are 50°each, two of its iterior angles are 127° and 135°,and the remaining interior angles are 173°each. Find the value of n.
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Use all exterior angles:
Three of the exterior angles of an n-sided polygon are 50°each, two of its exterior angles are 53° and 45°,and the remaining exterior angles are 7°each. Find the value of n
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Add the given angles
3*50 + 53 + 45 + x*7 = 360
248 + x*7 = 360
7x = 112
x = 16 angles
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Add the # of angles ( = n, # of sides)
3 + 1 + 1 + 16 = 21 sides
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the sum of the exterior angles of a polygon is always 360.
you have 3 exterior angles of 50 degrees = 150 degrees.
each exterior angle of a polygon is supplemental to its corresponding interior angle.
you have one interior angle of 127 degrees subtracted from 180 degrees equals one exterior angle of 53 degrees
you have one interior angle of 135 degrees subtracted from 180 degrees equals one exterior angle of 45 degrees.
altogether, you have 5 exterior angles with a sum of 248 degrees.
since the sum of all the exterior angles must be equal to 360 degrees, you have 360 - 248 = 112 degrees missing.
since the remaining interior angles are 173 degrees each, then the remaining exterior angle has to be 180 - 173 = 7 degrees each.
therefore, 112 / 7 = 16 exterior angles missing.
the total number of exterior angles is therefore 5 plus 16 = 21, bringing the total number of exterior angles degrees equal to 248 plus 112 = 360.
the value of n therefore has to be 16 plus 5 = 21.

it doesn't matter how many sides the polygon has; the sum of the exterior angles is always 360.





Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Three of the exterior angles of an n-sided polygon are 50°each, two of its iterior angles are 127° and 135°,and the remaining interior angles are 173°each. Find the value of n.
Since 3 of the exterior angles are 50o each, these sum to 150o (50 * 3). So, n - 3 angles remain.

Since 2 interior angles are 127o and 135o each, their exterior angles are 53o and 45o, respectively. So, n - 3 - 2, or n - 5 angles remain.

Since remaining n - 5 INTERIOR angles are 173o each, then remaining n - 5 EXTERIOR angles are 7o (180 - 173) each, and total 7(n - 5), or (7n - 35)o

Since the sum of the exterior angles of any polygon, is 360o, we now get: 150 + 53 + 45 + 7n - 35 = 360

213 + 7n = 360

7n = 360 - 213

7n = 147

Number of sides, or  

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