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.
