SOLUTION: The measure of the largest angle of a triangle is twice the measure of the smallest angle and 20 more than the measure of the third angle. find the measure of each angle.

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Question 243948: The measure of the largest angle of a triangle is twice the measure of the smallest angle and 20 more than the measure of the third angle. find the measure of each angle.
Answer by richwmiller(17219) About Me  (Show Source):
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The measure of the largest angle of a triangle is twice the measure of the smallest angle and 20 more than the measure of the third angle. find the measure of each angle.
answer:
plan: remember the angles of a triangle add up to 180 degrees.
let a= first angle (largest)
b=second angle (smallest)
c=third angle
a=2*b
solve for b in terms of a
b=1/2a
a=20+c
solve for c in terms of a
c=a-20
a+b+c=180
substitute
a+(1/2a)+(a-20)=180
2.5a-20=180
2.5a=200
multiply by 10
25*a=2000
factor 2000 for easier division
2000=100*20
2000=(25*4)*20
25*a=2000
25*a= (25*4)*20
divide by 25
a=80 degrees
b=40 degrees (1/2 a)
c=60 degrees (a-20)
check
80+40+60=180