Answer: 1. Sum of the interior angles = 720° 2. (6x) + (5x + 26.5) + (7x - 8) + (4x + 21.5) + (5x + 19) + (10x + 13.5) = 720 3. Angle A = 6x = 6(17.5) = 105 Angle B = (5x + 26.5) = 114 Angle C = (7x - 8) = 114.5 Angle D = (4x + 21.5) = 91.5 Angle E = (5x + 19) = 106.5 Angle F = (10x + 13.5) = 188.5
Step-by-step explanation: 1. The sum of the interior angles = (The number of sides - 2) times 180 The sum of the angles of this polygon with 6 sides is 6 - 2) times 180 = 720°. 2. ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720° (6x) + (5x + 26.5) + (7x - 8) + (4x + 21.5) + (5x + 19) + (10x + 13.5) = 720 37x + 72.5 = 720 Simplify adding x terms and numbers) 37x = 647.5 Subtract 72.5 from both sides x = 17.5 Dividing both sides by 37
Solve for each angle using x = 17.5 3. Angle A = 6x = 6(17.5) = 105 Angle B = (5x + 26.5) = 114 Angle C = (7x - 8) = 114.5 Angle D = (4x + 21.5) = 91.5 Angle E = (5x + 19) = 106.5 Angle F = (10x + 13.5) = 188.5
