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
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees
50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees
46°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees
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To find the measures of each angle in the triangle, we can use the Triangle Angle Sum Theorem, which 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 measures of the angles:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide both sides by 17:
x = 10
Now we can substitute the value of x back into the expressions for each angle to find their measures:
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 correct answer is: 46 degrees, 49 degrees, and 85 degrees.