Question
if 3 angle measures equal (8x+5) (5x-1) and (4x+6)Use the triangle angle sum Theorem To find the measure of each angleFor the triangle
Answers
GPT 3.5
The sum of the angles in a triangle is always 180 degrees.
Let the three angle measures be A, B, and C.
We are given that A = B = C = (8x+5)(5x-1)(4x+6).
Therefore, using the triangle angle sum theorem:
A + B + C = 180
(8x+5)(5x-1) + (8x+5)(5x-1) + (4x+6) = 180
Combining like terms:
(8x+5)(5x-1) + (8x+5)(5x-1) + (4x+6) - 180 = 0
Expanding:
(40x^2 - 8x + 25x - 5) + (40x^2 - 8x + 25x - 5) + 4x + 6 - 180 = 0
Combining like terms again:
80x^2 + 42x - 354 = 0
This is a quadratic equation, which can be factored as:
2(40x^2 + 21x - 177) = 0
Now, we can solve for x by factoring or using the quadratic formula. Once we have the value of x, we can substitute it back into the expressions for A, B, and C to find their respective measures.
Let the three angle measures be A, B, and C.
We are given that A = B = C = (8x+5)(5x-1)(4x+6).
Therefore, using the triangle angle sum theorem:
A + B + C = 180
(8x+5)(5x-1) + (8x+5)(5x-1) + (4x+6) = 180
Combining like terms:
(8x+5)(5x-1) + (8x+5)(5x-1) + (4x+6) - 180 = 0
Expanding:
(40x^2 - 8x + 25x - 5) + (40x^2 - 8x + 25x - 5) + 4x + 6 - 180 = 0
Combining like terms again:
80x^2 + 42x - 354 = 0
This is a quadratic equation, which can be factored as:
2(40x^2 + 21x - 177) = 0
Now, we can solve for x by factoring or using the quadratic formula. Once we have the value of x, we can substitute it back into the expressions for A, B, and C to find their respective measures.