Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6 , then
sum = 180° × 4 = 720°
sum the 6 angles and equate to 720
6x + 5x + 26.5 + 7x - 8 + 4x + 21.5 + 5x + 19 + 10x + 13.5 = 720 , that is
37x + 72.5 = 720 ( subtract 72.5 from both sides )
37x = 647.5 ( divide both sides by 37 )
x = 17.5
then
∠ A = 6x = 6(17.5) = 105°
∠ B = 5x + 26.5 = 5(17.5) + 26.5 = 87.5 + 26.5 = 114°
∠ C = 7x - 8 = 7(17.5) - 8 = 122.5 - 8 = 114.5°
∠ D = 4x + 21.5 = 4(17.5) + 21.5 = 70 + 21.5 = 91.5°
∠ E = 5x + 19 = 5(17.5) + 19 = 87.5 + 19 = 106.5°
∠ F = 10x + 13.5 = 10(17.5) + 13.5 = 175 + 13.5 = 188.5°
