Question 526642: In a rancher's pentagonal plot of land, when interior angles are put in decreasing
Order, each differs from the next by 10 degrees. Find the measure of the smallest interior
Angle of the field to the nearest tenth of a degree. The multiple choice is...
A: 88.0
B: 86.5
C: 128.0
D: 108.0
Please explain your answer!! Thank u:)
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The interior angles of a polygon = 180*(n-2), where n = number of sides.
With a pentagon, there are 180*(5-2) = 180*3 = 540 interior degrees, spread across 5 angles.
If the pentagon is a regular pentagon, all of the angles are 108 degrees.
.
But we are told it is not a regular pentagon.
.
x = measure of the largest angle.
x -10 = second
x -20 = third
x -30 = fourth
x -40 = fifth
.
5x -100 = 540
5x = 640
x = 128 is the largest angle
x -10 = 118
x -20 = 108
x -30 = 98
x -40 = 88
.
Check the sum of angles.
88 + 98 + 108 + 118 + 128 = 540
Correct.
.
Answer: The measure of the smallest angle is 88 degrees.
.
Done.
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