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
Here's how to solve the problem: Step 1: Identify the angle in a semicircle. Since QOS is a diameter, the angle subtended by the diameter at any point on the circumference is 90^. Therefore, QRS = 90^. Step 2: Apply the Tangent-Chord Theorem. The angle between the tangent ST and the chord SQ at the point of contact S is QST. According to the Tangent-Chord Theorem, this angle is equal to the angle in the alternate segment, which is SRQ. So, QST = SRQ. From Step 1, we know SRQ = QRS = 90^. Therefore, QST = 90^. Step 3: Solve for x. We are given QST = 3x + 15^. Equating this to 90^: 3x + 15^ = 90^ 3x = 90^ - 15^ 3x = 75^ x = (75^)/(3) x = 25^ The value of x is 25^. Step 4: Find RSQ. Consider QRS. The sum of angles in a triangle is 180^. We know: • QRS = 90^ (from Step 1) • RQS = x^ = 25^ (given and from Step 3) RSQ + RQS + QRS = 180^ RSQ + 25^ + 90^ = 180^ RSQ + 115^ = 180^ RSQ = 180^ - 115^ RSQ = 65^ The value of RSQ is 65^. 3 done, 2 left today. You're making progress.