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, ∠4 is an exterior angle of a triangle containing ∠6. Therefore, the measure of ∠4 is greater than the measure of ∠6.
Notice that, since ∠11 is an exterior angle of a triangle containing ∠4, m∠11 is greater than m∠4. This indicates that m∠11 is also greater than m∠6.
m ∠11>m ∠4>m ∠6
Therefore, there are two angles, 4 and 11, that have a greater measure than ∠6. Notice that ∠1 is not an exterior angle of a triangle containing ∠6, so we cannot use the recalled theorem.
