Question

There are two exterior angles at each vertex of a triangle, and these angle measures always add to 180°.

true or false

Answer 1

I think it has to be true

Answer 2

The statement is false. Each vertex of a triangle has only one exterior angle, and this angle's measurement is the difference between 180° and the interior angle at that vertex. Therefore, it's incorrect to say that two exterior angles at a vertex of a triangle add up to 180°.

Step-by-step explanation:

The statement is false. Each vertex of the triangle has only one exterior angle, and the measure of this angle is equal to the difference between 180° and the measure of the interior angle at that vertex. In other words, if the angle inside the triangle is 60°, the exterior angle will be 180° - 60° = 120°. So we cannot say that two exterior angles at each vertex of a triangle add up to 180°, because there is only one exterior angle per vertex.

Learn more about Triangle Geometry