Which angles are corresponding remote angles to ∠ 7?
∠ 5 and ∠ 9
Practice makes perfect
In this exercise we want to use the Exterior Angle Inequality Theorem to list all of the angles that has a measure greater than the measure of ∠ 7. 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, ∠ 7 is an interior angle of △ MNL. Because ∠ 5 and ∠ 9 do not share a vertex or corner of the triangle with ∠ 7, they are the corresponding remote angles. Now, let's 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 ∠ 5 and ∠ 9 are the corresponding remote angles of ∠ 7. Therefore, the theorem allows us to conclude that ∠ 5 and ∠ 9 have greater measures than ∠ 7.
