Answer:
x = 29
∠A = 174°
∠B = 132°
∠C = 203°
∠D = 118°
∠E = 73°
∠F = 20°
Step-by-step explanation:
Sum of interior angles of an irregular polygon = (n - 2) x 180°
where n = number of sides
The polygon has 6 sides,
therefore the sum of the interior angles = (6 - 2) x 180° = 720°
Add together all the angles, equal them to 720° and solve for x:
∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720
(6x) + (3x + 45) + (7x) + (4x + 2) + (2x + 15) + (x - 9) = 720
6x + 3x + 45 + 7x + 4x + 2 + 2x + 15 + x - 9 = 720
6x + 3x + 7x + 4x + 2x + x + 45 + 2 + 15 -9 = 720
23x + 53 = 720
23x = 720 - 53 = 667
x = 667/23 = 29
Now we have found the value of x, substitute this into the expression for each angle:
∠A = 6x = 6 x 29 = 174°
∠B = 3x + 45 = (3 x 29) + 45 = 132°
∠C = 7x = 7 x 29 = 203°
∠D = 4x + 2 = (4 x 29) + 2 = 118°
∠E = 2x + 15 = (2 x 29) + 15 = 73°
∠F = x - 9 = 29 - 9 = 20°
