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: Relate the angle at the center to the angle at the circumference. The angle subtended by an arc at the center is twice the angle subtended by the same arc at the circumference. For arc PR, the angle at the center is PSR and the angle at the circumference is PQR. PSR = 2 × PQR Substitute the given expression for PQR: PSR = 2(2x - 40^) = 4x - 80^ Step 2: Use the property of a diameter. Since PT is a diameter and S is the center, P, S, and T are collinear. Therefore, PST is a straight angle, which means PST = 180^. The angles PSR and RST are adjacent angles on this straight line. PSR + RST = 180^ Step 3: Substitute the expressions and solve for x. Substitute the expressions for PSR and RST into the equation from Step 2: (4x - 80^) + (x - 8^) = 180^ Combine like terms: 5x - 88^ = 180^ Add 88^ to both sides: 5x = 180^ + 88^ 5x = 268^ Divide by 5: x = (268)/(5) x = 53.6 Got more? Send 'em!