The angles of a hexagon are x + 10°, 2x + 20°, 2x - 20°, 3x - 50°, x + 40° and x + 20°. Find x.

According to the properties of a polygon, if a polygon has n sides, then the sum of its interior angles is (2n - 4) x 90°.

For a hexagon with 6 sides, n = 6.

The sum of its interior angles is:

(2 x 6 - 4) x 90°

= (12 - 4) x 90°

= 8 x 90°

= 720°

It is given that the angles of the hexagon are x + 10°, 2x + 20°, 2x - 20°, 3x - 50°, x + 40° and x + 20°.

⇒ ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720°

⇒ (x + 10°) + (2x + 20°) + (2x - 20°) + (3x - 50°) + (x + 40°) + (x + 20°) = 720°

⇒ x + 10° + 2x + 20° + 2x - 20° + 3x - 50° + x + 40° + x + 20° = 720°

⇒ 10x + 20° = 720°

⇒ 10x = 720° - 20°

⇒ 10x = 700°

⇒ x = $\dfrac{700°}{10}$

⇒ x = 70°

Hence, the value of x is 70°.