Use the Exterior Angle Inequality to set a relation between the marked angles.
The angle marked at R is exterior to △ PQR. By the Exterior Angle Inequality we have that its measure is greater than m∠ Q. Therefore, the exterior angle cannot be congruent with ∠ Q, which is why the markings are incorrect.
Practice makes perfect
Let's draw triangle △ PQR and the exterior angle corresponding to vertex R.
By the Exterior Angle Inequality we have that m ∠ 1 > m∠ P and m ∠ 1 > m∠ Q. This implies that ∠ 1≆ ∠ Q, which is why the markings in the given diagram are incorrect.
