Let's begin with recalling the Exterior Angle Inequality Theorem. This theorem tells us that the measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.
Now, let's look at the given picture. As we can see, ∠11 is an exterior angle of a triangle containing ∠4 and ∠9. Therefore, the measures of angles 4 and 9 are less than the measure of ∠11.
Notice that, since ∠4 is an exterior angle of a triangle containing ∠2 and ∠6, the measures of ∠2 and ∠6 are less than m∠4. This indicates that m∠2 and m∠6 are also less than m∠11.
m ∠11 &> m ∠9
m ∠11 &> m ∠4 > m ∠2
m ∠11&> m ∠4 >m ∠6
Therefore, there are four angles, 2,4,6 and 9, that have measure less than ∠11.
