Sum

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.

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#### Solution

Angles of quadrilateral are,

(4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°

∴ 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 = 16°

Hence angles are,

(4x)° = (4 × 16)° = 64°

5(x + 2)° = 5(16 + 2)° = 90°

(7x - 20)° = (7 × 16 - 20)° = 92°

6(x + 3)° = 6(16 + 3) = 114°

Concept: Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles

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