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: Analyze PQS. Given PQS = 45^ and QPS = 45^. The sum of angles in a triangle is 180^. PSQ = 180^ - PQS - QPS PSQ = 180^ - 45^ - 45^ PSQ = 90^ This confirms that PS is perpendicular to QR. Step 2: Analyze PRS. Since PS QR, we have PSR = 90^. We are given PRT = 30^. Note that PRT is the same as PRS. So, in right-angled PRS: RPS = 180^ - PSR - PRS RPS = 180^ - 90^ - 30^ RPS = 60^ Step 3: Calculate SPT. From the diagram, point T lies on the line segment SR. Therefore, RPS is the sum of RPT and SPT. RPS = RPT + SPT We know RPS = 60^ (from Step 2) and we are given RPT = 30^. 60^ = 30^ + SPT SPT = 60^ - 30^ SPT = 30^ The value QS = 4.5 cm is not required to solve for SPT. The final answer is 30^.