Question 1186011
let a = the smallest angle
let b = the middle angle
let c = the largest angle.


in a triangle, the sum of all the angles is 180 degrees.
therefore:
a + b + c = 180
c = a^2 and b = 2a.
the formula becomes:
a + 2a + a^2 = 180
combine like terms to get:
3a + a^2 = 180
subtract 180 from both sides of the equation and order the terms in descending order of degree to get:
a^2 + 3a - 180 = 0
factor this quadratic equation to get:
(a + 15) * (a - 12) = 0
solve for a to get:
a = -15 or a = 12
since a has to be positive, then a = 12.
a^2 + 3a - 180 = 0 becomes 12^2 + 3*12 - 180 = 0 which becomes 144 + 36 - 180 = 0 which becomes 180 - 180 = 0 which becomes 0 = 0, confirming the value of 12 for a is good.
the sum of the angles was a^2 + 2a + a which is equal to 180.
this becomes 144 + 24 + 12 = 180 which becomes 180 = 180 which confirms the sum of the angles = 180 is true.
the biggest angle is 144 degrees and is equal to 12 squared.
the middle angle is 24 and is equal to 2 * 12.
the smallest angle is 12.
your solution is that the biggest angle is 144 degrees.