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Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)° , (3x+3)° , and (2x−7...Question
Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)° , (3x+3)° , and (2x−7)° .(1 point)
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GPT 3.5
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Therefore, we can set up an equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplifying, we have:
6x - 24 = 180
Adding 24 to both sides, we get:
6x = 204
Dividing both sides by 6, we get:
x = 34
Now we can substitute x = 34 back into the angles to find their values:
(x-20) = (34-20) = 14 degrees
(3x+3) = (3*34+3) = 105 degrees
(2x-7) = (2*34-7) = 61 degrees
Therefore, the largest angle is 105 degrees.
Therefore, we can set up an equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplifying, we have:
6x - 24 = 180
Adding 24 to both sides, we get:
6x = 204
Dividing both sides by 6, we get:
x = 34
Now we can substitute x = 34 back into the angles to find their values:
(x-20) = (34-20) = 14 degrees
(3x+3) = (3*34+3) = 105 degrees
(2x-7) = (2*34-7) = 61 degrees
Therefore, the largest angle is 105 degrees.