In this exercise we want to use the Exterior Angle Inequality Theorem to list all of the angles that has a measure less than the measure of ∠4. Let's start by analyzing the given diagram. For the purposes of the solution, we will name the vertices of the triangles.
As we can see, ∠4 is an exterior angle to △ KMN. Because ∠1 and ∠2 do not share a vertex or corner of the triangle with ∠4, these are the corresponding remote interior angles. Let's now recall the Exterior Angle Inequality Theorem.
Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.
We previously stated that angles ∠1 and ∠2 are the corresponding remote interior angles of ∠4. Therefore, the theorem allows us to conclude that ∠1 and ∠2 have greater measures than ∠4.
