The Triangle Angle Sum Theorem states that the sum of the angles of a triangle is always 180 degrees.
Therefore, we can set up the equation:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Combining like terms, we have:
5x + 8x + 4x - 1 + 5 + 6 = 180
17x + 10 = 180
Subtracting 10 from both sides:
17x = 170
Dividing both sides by 17:
x = 10
Now, we can substitute x back into the expressions for the angles:
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 measures of each angle in the triangle are 49 degrees, 85 degrees, and 46 degrees.
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.
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