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.
