Question

which is the measure of ∠r? 45° 120° 60° 75° 135° 165°

Explanation:

Step1: Find the measure of ∠PQR

The exterior - angle and the adjacent interior - angle of a triangle are supplementary. So, ∠PQR+120° = 180°. Then ∠PQR=180° - 120° = 60°.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In △PQR, we know that ∠P + ∠Q+∠R = 180°. Given ∠P = 45° and ∠Q = 60°. Substitute these values into the formula: 45°+60°+∠R = 180°.

Step3: Solve for ∠R

First, simplify the left - hand side of the equation: 105°+∠R = 180°. Then, subtract 105° from both sides: ∠R=180° - 105° = 75°.

Answer:

75°