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
50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
46°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees
42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees
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The Triangle Angle Sum Theorem states that the sum of the measures of the angles in any triangle is always 180 degrees.
Let's set up an equation using the given information:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide by 17:
x = 10
Now we can substitute the value of x back into each angle expression to find the measures of each angle:
5(10) - 1 = 50 - 1 = 49 degrees
8(10) + 5 = 80 + 5 = 85 degrees
4(10) + 6 = 40 + 6 = 46 degrees
Therefore, the measures of each angle for the triangle shown in the diagram are 49 degrees, 85 degrees, and 46 degrees.
So the correct answer is: 46°, 49°, and 85° (46 degrees , 49 degrees , and 85 degrees)