Use the information given in the following figure to find:

(i) x.

(ii) ∠B and ∠C.

(i) It is given that the angles of a quadrilateral are (3x - 5)°, (8x - 15)°, (2x + 4)° and 90°.

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

So,

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 90° + (2x + 4)° + (3x - 5)° + (8x - 15)° = 360°

⇒ 90° + 2x° + 4° + 3x° - 5° + 8x° - 15° = 360°

⇒ 74° + 13x° = 360°

⇒ 13x° = 360° - 74°

⇒ 13x° = 286°

⇒ x° = $\dfrac{286°}{13}$

⇒ x° = 22°

Hence, the value of x is 22.

(ii) ∠B = (2x + 4)°

= (2 $\times$ 22 + 4)°

= (44 + 4)°

= 48°

∠C = (3x - 5)°

= (3 $\times$ 22 - 5)°

= (66 - 5)°

= 61°

Hence, ∠B = 48° and ∠C = 61°.