To find the measures of each angle in the triangle, we can set up an equation using the Triangle Angle Sum Theorem. The theorem states that the sum of the angles in a triangle is always 180 degrees.
Given:
Angle 1 = (5x - 1) degrees
Angle 2 = (8x + 5) degrees
Angle 3 = (4x + 6) degrees
Setting up the equation:
(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 plug x = 10 into the equations for each angle to find their measures:
Angle 1 = (5(10) - 1) = 49 degrees
Angle 2 = (8(10) + 5) = 85 degrees
Angle 3 = (4(10) + 6) = 46 degrees
Therefore, the measures of each angle in the triangle are 46 degrees, 49 degrees, and 85 degrees.
The correct response is:
46 degrees, 49 degrees, and 85 degrees
Triangle Angle Sum Theorem Quick Check
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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
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
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
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