use the triangle sum theorem to find the angles for the triangle 5x + 4, 4x + 14, 6x - 3
To find the angles of the triangle with side lengths 5x + 4, 4x + 14, and 6x - 3, we need to first find the value of x by using the triangle sum theorem.
According to the triangle sum theorem, the sum of the interior angles of a triangle is always 180 degrees.
So, we can set up an equation by adding the three angles of the triangle:
(5x + 4) + (4x + 14) + (6x - 3) = 180
Combine like terms:
15x + 15 = 180
Subtract 15 from both sides:
15x = 165
Now, divide by 15 to find the value of x:
x = 11
Now that we have found the value of x, we can substitute it back into the expressions for the angles to find their values:
Angle 1: 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees
Angle 2: 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees
Angle 3: 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees
Therefore, the angles of the triangle with side lengths 5x + 4, 4x + 14, and 6x - 3 are 59 degrees, 58 degrees, and 63 degrees.