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: Apply the Alternate Segment Theorem. The angle between the tangent MP and the chord NS at the point of contact N is equal to the angle subtended by the chord NS in the alternate segment. NRS = SNP Given SNP = 74^, so: NRS = 74^ Step 2: Use the property of equal chords. We are given that |NR| = |RS|. This means that triangle NRS is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. Therefore, the angle opposite side RS ( RNS) is equal to the angle opposite side NR ( NSR). RNS = NSR Step 3: Use the sum of angles in a triangle. The sum of angles in any triangle is 180^. For NRS: NRS + RNS + NSR = 180^ Substitute the values from Step 1 and Step 2: 74^ + RNS + RNS = 180^ 74^ + 2 RNS = 180^ Step 4: Solve for RNS. Subtract 74^ from both sides: 2 RNS = 180^ - 74^ 2 RNS = 106^ Divide by 2: RNS = (106^)/(2) RNS = 53^ Send me the next one 📸