Question

I am doing Polygons with Algebra and I have a irregular shape with letters on each point

A=x
B=130°
C=x+20°
D=120°
E=140°
F=x-20°
G=150°
Find the value of x, and use the 7 block chart to figure out answer for interior and exterior, and the equation.

Answer 1

Explanation:

Number of side = n = 7

Sum of interior angles of 'n' sided polygon = (n - 2) *180

= (7 - 2)* 180

= 5 * 180

= 900

x + 150 + x -20 + 140 + 120 + x + 20 + 130 = 900

Combine like terms

x +x +x + 150 - 20 + 140 + 120 + 20 +130 = 900

3x + 540 = 900 {Subtract 540 from both sides}

3x = 900 - 540

3x = 360 {Divide both sides by 3}

x = 360/3

x = 120

Interior angle Exterior angle

∠A = 120 180 - 120 = 60

∠B = 130 180 - 130 = 50

∠C = 120 + 20 = 140 180 - 140 = 40

∠D = 120 180 - 120 = 60

∠E = 140 180 - 140 = 40

∠F = 120 - 20 = 100 180 -100 = 80

∠G = 150 180 - 150 = 30