In triangle PQR, the exterior angles at Q and R measure 128° and 112°, respectively. Determine the measure of interior angle ∠P.

The correct answer is 60°.

To find the measure of the interior angle ∠P in triangle PQR, we can use the concept of linear pairs of angles and the angle sum property of a triangle.

Step 1: Find the interior angles at vertices Q and R.
An interior angle and its adjacent exterior angle lie on a straight line and form a linear pair. Therefore, their sum is always equal to 180°.

$\angle Q=180°-128°=52°$

$\angle R=180°-112°=68°$

Step 2: Apply the angle sum property of a triangle.
The sum of all three interior angles in any triangle is equal to 180°.

$\angle P+\angle Q+\angle R=180°$

Substitute the calculated measures of interior angles ∠Q and ∠R into the equation:

$\angle P+52°+68°=180°$

$\angle P+120°=180°$

Subtract 120° from both sides to solve for ∠P:

$\angle P=180°-120°=60°$

Thus, the measure of interior angle ∠P is 60°.