Final answer:
The sum of the interior angles of a triangle is 180 degrees, and by using linear pairs, we can prove that the sum of the exterior angles is 360 degrees. Each exterior angle forms a linear pair with its interior angle, and the sum of all three exterior angles equals that of three straight lines, which is 360 degrees.
Step-by-step explanation:
When thinking about a triangle, we know that it is a three-sided figure on a plane, and according to LibreTexts, the sum of its interior angles adds up to 180 degrees. To show that the sum of the exterior angles of a triangle is 360 degrees, we can use linear pairs. Each exterior angle forms a linear pair with its corresponding interior angle, meaning the two angles add up to 180 degrees since they are supplementary. Since there are three angles in a triangle, we have three linear pairs. Adding all three exterior angles should give us the same amount as adding up three straight lines, which is 360 degrees. This clearly demonstrates the interior angles add up to 180 degrees, and the exterior angles add up to 360 degrees.
An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles, and this property helps us understand the sum of the exterior angles. Since each corner of a triangle adds an exterior angle that equals the sum of the opposite interior angles, the total sum of exterior angles must be 360 degrees - equal to going once around a full circle.