Question 468818: Find the measure of the indicated exterior angle.
∠x = (4n - 20)°, ∠y = (n + 10)°, ∠z = (130 - 5n)°
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = (4n-20)
y = (n+10)
z = (130 - 5n)
the sum of the angles in a triangle is 180 degrees.
since x, y, and z are all interior angles of the triangle, then they must add up to 180 degrees.
you get:
(4n-20) + (n+10) + (130-n) = 180
remove parentheses to get:
4n - 20 + n + 10 + 130 - n = 180
combine like terms to get:
4n + 120 = 180
subtract 120 from both sides of this equation to get:
4n = 60
divide both sides of this equation by 4 to get:
n = 15
since you know what n is, you can now find each of the angles.
4n-20 = 60-20 = 40
n+10 = 15+10 = 25
130-n = 130-15 = 115
sum of the angles is 40 + 25 + 115 = 65 + 115 = 180
you are asked to find an exterior angle.
you can find the exterior angle of any of the interior angle by just subtracting that angle from 180 degrees.
exterior angle of 40 degrees = 180 - 40 = 140 degrees
exterior angle of 25 degrees = 180 - 25 = 155 degrees
exterior angle of 115 degrees = 180 - 115 = 65 degrees
since the sum of the exterior angles of a polygon is equal to 360 degrees, then 140 + 155 + 65 must be equal to 360 if we did this correctly.
it is and we did.
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