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 the relationship between the given angles. The lines AB and CD are parallel, and they are intersected by a transversal line. The angles (3x + 15^) and (2x + 30^) are consecutive interior angles (also known as same-side interior angles). Step 2: Apply the property of consecutive interior angles. When two parallel lines are cut by a transversal, the consecutive interior angles are supplementary, meaning their sum is 180^. (3x + 15^) + (2x + 30^) = 180^ Step 3: Solve the equation for x. Combine the terms with x and the constant terms. 5x + 45^ = 180^ Subtract 45^ from both sides. 5x = 180^ - 45^ 5x = 135^ Divide by 5. x = (135^)/(5) x = 27^ The value of x is 27. Send me the next one 📸