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
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°
To find the measures of each angle, we can set up the equation using the Triangle Angle Sum Theorem:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Combining like terms, we have:
17x + 10 = 180
Subtracting 10 from both sides:
17x = 170
Dividing both sides by 17:
x = 10
Now we can substitute x = 10 into the expressions for each angle:
Angle 1 = 5x - 1 = 5(10) - 1 = 49°
Angle 2 = 8x + 5 = 8(10) + 5 = 85°
Angle 3 = 4x + 6 = 4(10) + 6 = 46°
Therefore, the measures of each angle for the triangle shown in the diagram are 46°, 49°, and 85°.