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 angles of a triangle is always 180 degrees.
Therefore, we can set up the equation:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Combining like terms, we have:
5x + 8x + 4x - 1 + 5 + 6 = 180
17x + 10 = 180
Subtracting 10 from both sides:
17x = 170
Dividing both sides by 17:
x = 10
Now, we can substitute x back into the expressions for the angles:
Angle 1: 5x - 1 = 5(10) - 1 = 50 - 1 = 49 degrees
Angle 2: 8x + 5 = 8(10) + 5 = 80 + 5 = 85 degrees
Angle 3: 4x + 6 = 4(10) + 6 = 40 + 6 = 46 degrees
Therefore, the measures of each angle in the triangle are 49 degrees, 85 degrees, and 46 degrees.