Ext angles in triangles

Quin és el resultat de la suma de tots els angles exteriors d'un triangle?

Un angle exterior d'un triangle és igual a la suma de quins angles internals?

Quin és el nom del teorema que estableix que la mesura d'un angle exterior d'un triangle és igual a la suma de les mesures dels dos angles internals no adjacents?

Quin és el nom del teorema que estableix que la mesura d'un angle exterior d'un triangle és igual a la mesura de l'angle intern remot?

En quin cas els angles exteriors d'un triangle són suplementaris?

Quin és l'ús més comú dels angles exteriors en la vida real?

Si un angle exterior d'un triangle és de 120°, quin és el valor de l'angle intern adjacent?

Quin és el valor de la suma de tots els angles interns d'un triangle?

Exterior Angles in Triangles

Definition

An exterior angle is an angle formed by extending a side of a triangle.
It is exterior to the triangle and lies outside the triangle.

Properties

The sum of the exterior angles of a triangle is 360°.
Each exterior angle is equal to the sum of the two non-adjacent interior angles.
Exterior angles are supplementary to their adjacent interior angles (i.e., they add up to 180°).

Theorems

Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Remote Interior Angle Theorem: The measure of an exterior angle is equal to the measure of the remote interior angle.

Applications

Exterior angles are used in trigonometry and geometry to solve problems involving right triangles and oblique triangles.
They are also used in real-world applications such as architecture, engineering, and design.

Examples

In a triangle ABC, the exterior angle at vertex A is 120°. If the interior angle at A is 40°, what are the measures of the other two interior angles?
In a triangle DEF, the exterior angle at vertex D is 150°. If the interior angle at D is 30°, what are the measures of the other two interior angles?