The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if one of the interior angles is 30 degrees, the sum of the other two interior angles must be 180 - 30 = 150 degrees.
An exterior angle of a triangle is equal in measure to the sum of the two opposite interior angles. Therefore, if one of the exterior angles is 40 degrees, the sum of the two opposite interior angles must be 40 degrees.
Let the other two interior angles be x and y. We can set up the following equation based on our information:
x + y = 40
We also know that the sum of the other two interior angles is 150. Therefore, we can set up the additional equation:
x + y = 150
Since both equations are equal to x + y, we can set them equal to each other:
40 = 150
This equation is not true, so there is no solution. Therefore, the remaining interior angles cannot be determined with the given information.
One of the interior angles of a triangle is equal to 30 degrees, and one of the exterior angles is equal to 40 degrees. Find the remaining interior angles of this triangle.
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