Question

use the diagram to show that the sum of the measures of the exterior angles of a triangle, one at each vertex, is 360. first identify the linear pairs in the diagram. ∠1 and ∠4 are a linear pair. ∠2 and ∠5 are a linear pair. ∠3 and ∠6 are a linear pair. what is the sum of the angle measures in a linear pair?

Explanation:

Step1: Recall linear pair definition

A linear pair of angles are adjacent angles that form a straight line. A straight line has an angle measure of \(180^\circ\) (a straight angle).

Step2: Determine sum of linear pair

By the definition of a linear pair (adjacent angles forming a straight line), the sum of the measures of angles in a linear pair is equal to the measure of a straight angle, which is \(180^\circ\).

Answer:

\(180^\circ\) (or 180 degrees)