The sum of the exterior angles of any polygon, including a triangle, is always 360 degrees. If the sum of the exterior angles of the isosceles triangle is given as 240 degrees, this value does not align with the property of exterior angles.
However, assuming that we interpret the problem correctly, we can derive the interior angles as follows:
The sum of the exterior angles being 240 degrees suggests that the triangle is not a typical triangle or there is some confusion, but for clarity, let’s consider an isosceles triangle where the correct statement should be that the sum of the degrees of the interior angles is 180 degrees.
In an isosceles triangle, let’s denote the angles as follows:
- The two equal angles as \( x \)
- The base angle as \( y \)
The equation for the sum of interior angles is: \[ 2x + y = 180 \]
To find the specific measures of the angles, we need another relationship. Given that the exterior angle corresponding to the distinct interior angle \( y \) is the sum of the other two interior angles \( 2x \): \[ y + 2x = 240 \]
Now we have two equations:
- \( 2x + y = 180 \)
- \( y + 2x = 240 \)
From the first equation, we can express \( y \) in terms of \( x \): \[ y = 180 - 2x \]
Substituting \( y \) into the second equation: \[ (180 - 2x) + 2x = 240 \]
This simplifies to: \[ 180 = 240 \]
This equation is incorrect, which indicates a contradiction in the assumption; thus it implies that we must reevaluate the initial condition about the sum of the exterior angles.
The essence remains that the sum of the interior angles in any triangle is fixed at 180 degrees.
Conclusion: To resolve this, you might need to further clarify the initial conditions, as the given information for calculating the angles in a standard triangle context is invalid if assuming the sum of exterior angles as less than 360. Could you verify this?
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