Question

Each angle of a quadrilateral is x + 5°. Find:

(i) the value of x

(ii) each angle of the quadrilateral.

Give the special name of the quadrilateral taken.

Answer 1

(i) We have,

∠A + ∠B + ∠C + ∠D = 360°

∵ We know that the sum of interior angles of a quadrilateral is 360°

∴ ∠A + ∠B + ∠C + ∠D = 360°

⇒ x + 5° + x + 5° + x + 5° + x + 5° = 360°

⇒ 4x + 20° = 360°

⇒ 4x = 360° - 20°

⇒ ${\displaystyle \text{x}=\frac{340°}{4}=85°}$

(ii) Each angle of the quadrilateral ABCD = x + 5°

= 85° + 5°

= 90°

The name of the given quadrilateral is a rectangle.