HELP ASAP Professor Plum is putting a brick border around his irregular shaped garden. Before installing
the border, Professor Plum must cut the bricks to fit the angles of the garden. Use the given
measures to answer the question.
∡ = (6)°
∡ = (3 + 45)°
∡ = (7)°
∡ = (4 + 2)°
∡ = (2 + 15)°
∡ = ( − 9)°
What are the angle measures of each vertex of the garden? Show your work

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°

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