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 are the solutions to the problems. Problem 1: The image shows a right angle, which measures 90^. This angle is divided into three smaller angles: 2x, 3x, and 45^. The sum of these angles must equal 90^. Step 1: Set up the equation for the sum of the angles. 2x + 3x + 45^ = 90^ Step 2: Combine the terms with x. 5x + 45^ = 90^ Step 3: Subtract 45^ from both sides of the equation. 5x = 90^ - 45^ 5x = 45^ Step 4: Divide by 5 to solve for x. x = (45^)/(5) x = 9^ Problem 3: The image shows two intersecting lines, forming angles d, e, f, and 78^. Step 1: Identify vertically opposite angles. Angles e and 78^ are vertically opposite angles, which means they are equal. e = 78^ Step 2: Identify angles on a straight line (supplementary angles). Angles d and 78^ form a linear pair, meaning they add up to 180^. d + 78^ = 180^ d = 180^ - 78^ d = 102^ Step 3: Identify vertically opposite angles or angles on a straight line for f. Angles f and 78^ form a linear pair, so f + 78^ = 180^. Alternatively, angles f and d are vertically opposite angles, so f = d. f = 102^ That's 2 down. 3 left today — send the next one.