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 calculate the size of R_1 and S: Given: In PQS, R is the mid-point of QS. PR = QR. Q = 56^. Step 1: Calculate R_1. Since PR = QR, PQR is an isosceles triangle. The angles opposite the equal sides are equal. QPR = Q = 56^ The sum of angles in a triangle is 180^. In PQR: R_1 + QPR + Q = 180^ R_1 + 56^ + 56^ = 180^ R_1 + 112^ = 180^ R_1 = 180^ - 112^ R_1 = 68^ Step 2: Calculate S. Angles R_1 and R_2 (which is PRS) are supplementary angles because they form a straight line at R on QS. R_1 + R_2 = 180^ 68^ + R_2 = 180^ R_2 = 180^ - 68^ R_2 = 112^ Since R is the mid-point of QS, QR = RS. We are given PR = QR. Therefore, PR = RS. This means PRS is an isosceles triangle. The angles opposite the equal sides are equal: RPS = S The sum of angles in PRS is 180^: R_2 + RPS + S = 180^ 112^ + S + S = 180^ 112^ + 2S = 180^ 2S = 180^ - 112^ 2S = 68^ S = (68^)/(2) S = 34^ 3 done, 2 left today. You're making progress.