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 â–³ 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.
