Question

given the diagram below, gitta writes \\(m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ\\). which of the following reasons allows her to write this statement?

a. triangle sum theorem
b. exterior angles theorem
c. definition of linear pair
d. subtraction property of equality

Explanation:

Identify the angles in the statement

$$ \angle 1, \angle 2, \text{ and } \angle 3 \text{ are the interior angles of the triangle shown in the diagram.} $$

Relate the sum of interior angles to geometric theorems

$$ m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ $$

This statement states that the sum of the measures of the interior angles of a triangle is \(180^\circ\), which is the definition of the Triangle Sum Theorem.

Answer:

• A. Triangle sum theorem (Correct answer)
• B. Exterior angles theorem
• C. Definition of linear pair
• D. Subtraction property of equality