Final answer:
To find the remaining interior angles of a triangle, we can use the fact that the exterior angle is equal to the sum of the two non-adjacent interior angles.
Step-by-step explanation:
In a triangle, the sum of all interior angles is always 180 degrees. Given that one of the interior angles is 30 degrees and one of the exterior angles is 40 degrees, we can find the remaining interior angles.
To find the remaining interior angles, we can use the fact that the exterior angle is equal to the sum of the two non-adjacent interior angles. So, if one of the exterior angles is 40 degrees, then the sum of the two non-adjacent interior angles must also be 40 degrees.
Let's call the remaining interior angles x and y. We have the equation x + y = 40. Since we know that the sum of all interior angles is 180 degrees, we can also write the equation x + y + 30 = 180.
Solving for x and y, we have the following system of equations:
x + y = 40
x + y + 30 = 180
Subtracting the first equation from the second, we get:
(x + y + 30) - (x + y) = 180 - 40
30 = 140
This equation is not true, so there must be an error in the problem statement or calculations. Please check the problem again and provide the correct information so that I can assist you further.