In any triangle, when you extend one of its sides, you create an exterior angle. This exterior angle has a special relationship with the two interior angles that are not adjacent to it. The measure of the exterior angle is indeed equal to the sum of the measures of the two opposite interior angles.
This can be understood using the following reasoning: The sum of the interior angles of any triangle is always 180 degrees. When you extend one side, you form an exterior angle that, together with the adjacent interior angle, must equal 180 degrees. Thus, if you take that exterior angle and subtract the adjacent interior angle from 180 degrees, you’ll be left with the sum of the two opposite interior angles.
For example, if you have triangle ABC and you extend side BC to point D, the exterior angle at point C (angle ACD) will equal the sum of angles A and B (the two opposite interior angles) because:
Angle ACD = Angle A + Angle B
This rule is a fundamental property of triangles and is key in various geometric proofs and calculations.