In order to determine which angle out of ∠8, ∠10, and ∠11 has the greatest measure, let's analyze the diagram.
As we can see, ∠8 is an exterior angle, with ∠10 and the sum of ∠11 and ∠14 as its corresponding remote interior angles. According to the Exterior Angle Inequality Theorem, ∠8 is greater than either of its corresponding remote angles. Therefore, m∠8 > m∠10. Moreover, the following inequalities are true.
m∠8> m∠11+ m∠14
⇓
m∠8> m∠11 and m∠8 >m∠14
Finally, we have that ∠8 has the greatest measure out of ∠8, ∠10, and ∠11.
