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.
(1 point)
Responses
42°, 44°, and 79°
50°, 54°, and 93°
46°, 50°, and 85°
46°, 49°, and 85°
To use the Triangle Angle Sum Theorem, we know that the sum of the angles in a triangle is 180 degrees.
We can set up the equation:
(5x -1) + (8x + 5) + (4x + 6) = 180
Simplifying the equation:
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 angle measurements:
Angle 1: 5x - 1 = 5(10) - 1 = 50 - 1 = 49°
Angle 2: 8x + 5 = 8(10) + 5 = 80 + 5 = 85°
Angle 3: 4x + 6 = 4(10) + 6 = 40 + 6 = 46°
Therefore, the measures of each angle for the triangle shown in the diagram are 49°, 85°, and 46°. The correct answer is 46°, 49°, and 85°.