Final Answer:
The sum of the interior angles of triangle ∆ABC equals 180° because it adheres to the property that the total measure of the interior angles of any triangle is constant and equal to 180°.
Step-by-step explanation:
In any triangle, the sum of its interior angles remains constant at 180°. To prove this, consider triangle ∆ABC. By definition, a triangle comprises three angles, denoted as ∠A, ∠B, and ∠C. Using the fact that the total angle measure on a straight line is 180° (a straight angle), we can establish the relationship within triangle ∆ABC.
Firstly, ∠A and ∠B form a straight line when extended, creating a straight angle with a measure of 180°. Therefore, the sum of ∠A and ∠B within triangle ∆ABC must be less than 180°, leaving room for ∠C to fit within the total angle measure of 180°.
Additionally, considering ∠C with respect to the other angles, it completes the triangle, filling the remaining angle measure required to reach 180°. Hence, the sum of the interior angles of ∆ABC equals 180° due to the inherent property of triangles, ensuring that the combination of the three angles always totals to this fixed measure.
This fundamental property applies to all triangles, ensuring that regardless of their size or shape, the sum of their interior angles remains constant at 180°. Thus, in triangle ∆ABC, the total angle measure is fixed at 180°, reinforcing the proof that the sum of its interior angles always equals this constant value.