Angles of a quadrilateral are (4x)°, 5(x + 2)°, (7x - 20)° and 6(x + 3)°. Find:

(i) the value of x.

(ii) each angle of the quadrilateral.

(i) It is given that the angles of a quadrilateral are (4x)°, 5(x + 2)°, (7x - 20)° and 6(x + 3)°.

As we know, the sum of all angles in a quadrilateral is 360°.

So,

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ (4x)° + 5(x + 2)° + (7x - 20)° + 6(x + 3)° = 360°

⇒ 4x° + 5x° + 10° + 7x° - 20° + 6x° + 18° = 360°

⇒ 22x° + 8° = 360°

⇒ 22x° = 360° - 8°

⇒ 22x° = 352°

⇒ x° = $\dfrac{352°}{22}$

⇒ x° = 16°

Hence, the value of x is 16.

(ii) Each angle is (4x)°, 5(x + 2)°, (7x - 20)° and 6(x + 3)°:

= (4 $\times$ 16)°, 5(16 + 2)°, (7 $\times$ 16 - 20)° and 6(16 + 3)°

= 64°, 5(18)°, (122 - 20)° and 6(19)°

= 64°, 90°, 92° and 114°

Hence, the angles of the quadrilateral are 64°, 90°, 92° and 114°.