Final Answer:
The measure of the exterior angle at vertex K is 160°, thus the correct option is b.
Explanation:
According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. In this case, ∠J and ∠K are the two opposite interior angles of the triangle. As ∠J = 100° and ∠K = 80°, the sum of the two angles is 180°. Therefore, the measure of the exterior angle at vertex K is 180° - 80° = 160°.
The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. This theorem is based on the fact that the sum of the angles of a triangle is 180°. Therefore, when two opposite interior angles are known, it is possible to determine the measure of the exterior angle.
The exterior angle theorem is an important concept in geometry as it helps to determine the measure of one of the angles in a triangle when the measure of the other two angles are known. This theorem has a wide range of applications, from measuring angles in a triangle to finding the area of a triangle.
In conclusion, the measure of the exterior angle at vertex K is 160°, which can be determined by using the exterior angle theorem.