Question

HELP ASAP!!! 50 Points!!

Answer 1

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°