Question

Marisol claims that each pair of remote interior angles in a triangle has two exterior angles. Do you agree? Use a diagram to support your answer.

a. Yes,
b. No,

Answer 1

Marisol's claim that each pair of remote interior angles in a triangle has two exterior angles is incorrect. Each interior angle of a triangle has only one associated exterior angle, formed by extending one of the triangle's sides.

Step-by-step explanation:

The claim that each pair of remote interior angles in a triangle has two exterior angles is incorrect. In a triangle, there are three interior angles, and these angles add up to 180 degrees.

An exterior angle is formed by extending one side of the triangle. Each interior angle has just one exterior angle associated with it, not two. Therefore, there are three exterior angles in total, one for each side extended. To visualize this:

• Consider an interior angle of a triangle.
• Extend the side of the triangle that is adjacent to the considered angle, outward past the vertex of the angle.
• The angle that is outside the triangle, between the extended line and the adjacent side, is the exterior angle.

For each interior angle, only one such exterior angle exists; they are not in pairs. Hence, Marisol's claim is incorrect as each pair of remote interior angles does not have two exterior angles, but one each.