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°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees
42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees
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To solve this problem, we can set up the equation:
\(5x - 1 + 8x + 5 + 4x + 6 = 180\)
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:
\(5x - 1 = 5(10) - 1 = 50 - 1 = 49\) degrees
\(8x + 5 = 8(10) + 5 = 80 + 5 = 85\) degrees
\(4x + 6 = 4(10) + 6 = 40 + 6 = 46\) degrees
So the measures of each angle for the triangle are 49 degrees, 85 degrees, and 46 degrees.
Therefore, the correct answer is:
46 degrees, 49 degrees, and 85 degrees.