Question

PLEASEEE HELPPP 30 POINTSSS!!!

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.

Answer 1

174; 132; 203; 118; 73; 20°.

Explanation:

1) the sum of the internal angles of the given figure is:

S=180*(n-2), where 'n' is number of the angles.

2) according to the rule above the sum of all the internal angles is 720°;

3) according to the item 2, m∠A+m∠B+m∠C+m∠D+m∠E+m∠F=720°. If all the angles are known, then it is possible to re-write this equation as:

6x+(3x+45)+7x+(4x+2)+(2x+15)+(x-9)=720;

23x=667; ⇔ x=29.

4) if x=29, then m∠A=174; m∠B=132; m∠C=203; m∠D=118; m∠E=73; m∠F=20°.