SOLUTION: calculate the largest angle of a triangle in which one angle is eight times each other

Question 556170: calculate the largest angle of a triangle in which one angle is eight times each other

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sum of the angles of a triangle equals 180.
a = angle a
b = angle b
c = angle c
a + b + c = 180
a = 8b
a = 8c
this leads to:
8b + b + c = 180
8c + b + c = 180
simplify these equations to get:
9b + c = 180
b + 9c = 180
multiply the second equation by 9 to get:
9b + c = 180
9b + 81c = 1620
subtract the first equation from the second equation to get:
80c = 1440
divide both sides of this equation by 80 to get:
c = 18
since a = 8c, this means that a = 144.
since a = 8b, this means that b = a/8 which means that b = 18.
the angles of this triangle are:
a = 144
b = 18
c = 18
sum of the angles is 180
a is 8 times b and a is also 8 times c.
your answer is that the largest angle is 144 degrees.

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