Triangle Angle Sum Theorem Quick Check

Question

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Question
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

46°, 50°, and 85°
46 degrees , 50 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
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Answer 1

To find the measures of each angle for the triangle, we can set up the equation:

(5x - 1) + (8x + 5) + (4x + 6) = 180 degrees

Combine like terms:

17x + 10 = 180

Subtract 10 from both sides:

17x = 170

Divide both sides by 17:

x = 10

Now we can substitute x back into the expressions for each angle:

Angle 1: 5(10) - 1 = 49 degrees
Angle 2: 8(10) + 5 = 85 degrees
Angle 3: 4(10) + 6 = 46 degrees

So the correct answer is:

46 degrees, 49 degrees, and 85 degrees