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 Angel — been a while! Let's pick up where you left off. Step 1: Determine the number of sides of the polygon. The given shape has 6 sides, making it a hexagon. Step 2: Calculate the sum of the interior angles of a hexagon. The formula for the sum of interior angles of a polygon with n sides is (n-2) × 180^. For a hexagon, n=6. Sum of interior angles = (6-2) × 180^ = 4 × 180^ = 720^ Step 3: Identify all interior angles of the hexagon. • One angle is given as 80^. • Two angles are right angles, which are 90^ each. • One angle is given as 120^. • One angle is x^. • The remaining angle has an exterior angle of 15^. The interior angle is 180^ - 15^ = 165^. Step 4: Set up an equation using the sum of the interior angles. Summing all the interior angles and equating them to the total sum: 80^ + 90^ + 90^ + 120^ + x^ + 165^ = 720^ Step 5: Solve for x. Combine the known angles: (80 + 90 + 90 + 120 + 165)^ + x^ = 720^ 545^ + x^ = 720^ Subtract 545^ from both sides: x^ = 720^ - 545^ x^ = 175^ The value of x is 175^. Send me the next one 📸