SOLUTION: the size of the smallest angle of a triangle is 30% of the size of the largest angle.the size of the third angle is 20 degrees more than the smallest angle. Fund the size of each a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the size of the smallest angle of a triangle is 30% of the size of the largest angle.the size of the third angle is 20 degrees more than the smallest angle. Fund the size of each a      Log On


   

Question 156724: the size of the smallest angle of a triangle is 30% of the size of the largest angle.the size of the third angle is 20 degrees more than the smallest angle. Fund the size of each angle.
Answer by nerdybill(7384) About Me  (Show Source):
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the size of the smallest angle of a triangle is 30% of the size of the largest angle.the size of the third angle is 20 degrees more than the smallest angle. Fund the size of each angle.
.
Let x = largest angle
then from:"smallest angle of a triangle is 30% of the size of the largest angle"
.30x = smallest angle
and from:"20 degrees more than the smallest angle"
.30x+20 = 3rd angle
.
You're also suppose to know that the sum of the three interior angles of any triangle is 180:
x + .30x + .30x+20 = 180
1.6x + 20 = 180
1.6x = 160
x = 160/1.6
x = 100 deg (largest angle)
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smallest angle:
.30x = .30(100) = 30 deg
.
third angle:
.30x+20 = .30(100) + 20 = 50 deg