Use the image to answer the question.
A triangle is shown with its angles measuring left parenthesis 5 x minus 1 right parenthesis degrees, left parenthesis 8 x plus 5 right parenthesis degrees, and left parenthesis 4 x plus 6 right parenthesis degrees.
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.
The Triangle Angle Sum Theorem states that the sum of the measures of the angles in any triangle is always 180 degrees.
Let's use this theorem to find the measures of the angles in the given triangle.
We are given the measures of the angles as:
Angle 1: 5x - 1 degrees
Angle 2: 8x + 5 degrees
Angle 3: 4x + 6 degrees
According to the Triangle Angle Sum Theorem, the sum of these angles should be equal to 180 degrees.
So, we can write the equation:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Now, let's solve this equation to find the value of x.
Combine like terms:
5x + 8x + 4x - 1 + 5 + 6 = 180
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide both sides by 17:
x = 10
Now that we have found the value of x, we can substitute it back into the expressions for each angle to find their measures.
Angle 1: 5x - 1 = 5(10) - 1 = 49 degrees
Angle 2: 8x + 5 = 8(10) + 5 = 85 degrees
Angle 3: 4x + 6 = 4(10) + 6 = 46 degrees
Therefore, the measures of the angles in the triangle are:
Angle 1: 49 degrees
Angle 2: 85 degrees
Angle 3: 46 degrees