Final answer:
The question is incorrectly asserting that ∠1 and ∠2 are alternate interior angles, which they are not. To prove the Exterior Angle Theorem, one must show m∠1 + m∠2 = m∠4, which can be done using the fact that the sum of the interior angles of a triangle equals 180 degrees and that an exterior angle is supplementary to its adjacent interior angle.
Step-by-step explanation:
The question is addressing the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. However, the given statement “a. ∠1 and ∠2 are alternate interior angles, so m∠1 = m∠2” is incorrect since ∠1 and ∠2 are actually interior angles of the triangle and not alternate interior angles. The correct proof would involve demonstrating that m∠1 + m∠2 is indeed equal to m∠4 by considering that the sum of the angles in a triangle is 180 degrees and using the fact that an exterior angle is supplementary to its adjacent interior angle. Therefore, if m∠3 is the measure of the angle adjacent to ∠4 within the triangle, then m∠1 + m∠2 + m∠3 = 180 degrees and m∠3 + m∠4 = 180 degrees (since they are supplementary), leading to m∠1 + m∠2 = m∠4 after substituting the values.