This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
I will solve question 8. Question 8: In the diagram, |PQ| = |PR| = |RS| and RPS = 32^. Find QPR. Step 1: Analyze PRS. Given that |PR| = |RS|, PRS is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. Therefore, RSP = RPS. Since RPS = 32^, then RSP = 32^. Step 2: Find the exterior angle PRQ of PRS. The exterior angle of a triangle is equal to the sum of the two opposite interior angles. PRQ = RPS + RSP PRQ = 32^ + 32^ PRQ = 64^ Step 3: Analyze PQR. Given that |PQ| = |PR|, PQR is an isosceles triangle. Therefore, PQR = PRQ. From Step 2, we found PRQ = 64^. So, PQR = 64^. Step 4: Find QPR in PQR. The sum of angles in a triangle is 180^. QPR + PQR + PRQ = 180^ QPR + 64^ + 64^ = 180^ QPR + 128^ = 180^ QPR = 180^ - 128^ QPR = 52^ The value of QPR is 52^. The correct option is D. D. 52^ Drop the next question.