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
Step 1: Identify the given information from the problem statement and the diagram. • We are asked to calculate QRS. • We are given that |PQ| = |QS|. This means that triangle PQS is an isosceles triangle. • From the diagram, the angle PSQ is marked as 80^. Step 2: Use the property of the isosceles triangle PQS. Since PQ = QS, the angles opposite these sides in PQS are equal. The angle opposite side PQ is QSP. The angle opposite side QS is QPS. Therefore, QPS = QSP. Step 3: Substitute the known angle value. We are given PSQ = 80^, which is the same as QSP. So, QPS = 80^. Step 4: Use the property of a cyclic quadrilateral. The points P, Q, R, S lie on the circumference of the circle, forming a cyclic quadrilateral PQRS. In a cyclic quadrilateral, the sum of opposite angles is 180^. The angle opposite to QRS is QPS. Therefore, QRS + QPS = 180^. Step 5: Calculate QRS. Substitute the value of QPS from Step 3 into the equation from Step 4: QRS + 80^ = 180^ QRS = 180^ - 80^ QRS = 100^ The value of $\