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, ∠ 9 is an exterior angle to △ BCD. Because ∠ 6 and ∠ 7 do not share a vertex or corner of the triangle with ∠ 9, these are the corresponding remote interior angles.
Additionally, ∠ 9 is an exterior angle to △ ACD, as well. As we can see, ∠ CDA and ∠ DAC 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.
By this theorem, we can conclude that the measure of ∠ 9 is greater than the measures of ∠ 6, ∠ 7, ∠ 1, and ∠ 3. In other words, m∠ 1, m∠ 3, m∠ 6, and m∠ 7 are less than m∠ 9.
