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 parallel lines and given angles. We are given that PQ RT and QR SU. We are given PQR = 48^ and RTS = x. Step 2: Use the property of alternate interior angles for PQ RT. Consider the parallel lines PQ and RT intersected by the transversal QR. The angles PQR and QRT are alternate interior angles. Therefore, they are equal: QRT = PQR = 48^ Step 3: Use the property of consecutive interior angles for QR SU. Consider the parallel lines QR and SU intersected by the transversal RT. The angles QRT and RTS are consecutive interior angles (also known as co-interior angles). The sum of consecutive interior angles is 180^. So, we have: QRT + RTS = 180^ Step 4: Substitute the known values and solve for x. Substitute QRT = 48^ and RTS = x into the equation: 48^ + x = 180^ Subtract 48^ from both sides: x = 180^ - 48^ x = 132^ The value of x is 132^. 3 done, 2 left today. You're making progress.