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)° .
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Therefore, we have the equation: (x-20) + (3x+3) + (2x-7) = 180
Combining like terms, we get: 6x - 24 = 180
Adding 24 to both sides, we get: 6x = 204
Dividing both sides by 6, we get: x = 34
Now we can find the angle measures:
The largest angle is (3x+3)°, so substituting x = 34:
(3(34) + 3) = 102 + 3 = 105 degrees
Therefore, the largest angle in the triangle is 105 degrees.
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A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.
Find the measure of the smallest angle of the triangle.