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.
