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
Welcome back — been a while! Let's pick up where you left off. Step 1: Determine the sum of the interior angles of a pentagon. The sum of the interior angles of a polygon with n sides is given by the formula (n-2) × 180^. For a pentagon, n=5. Sum of angles = (5-2) × 180^ = 3 × 180^ = 540^ Step 2: Set up an equation using the given angles and the relationship between the remaining two angles. The given angles are 120^, 100^, and 108^. Let one of the remaining angles be x. The other remaining angle is three times the first, so it is 3x. The sum of all five angles must be 540^. 120^ + 100^ + 108^ + x + 3x = 540^ Step 3: Solve the equation for x. Combine the known angles and the terms with x: 328^ + 4x = 540^ Subtract 328^ from both sides: 4x = 540^ - 328^ 4x = 212^ Divide by 4: x = (212^)/(4) x = 53^ Step 4: Calculate the size of each of the remaining two angles. One angle is x: x = 53^ The other angle is 3x: 3x = 3 × 53^ = 159^ The remaining two angles are 53^ and 159^. Got more? Send 'em 📸