Question

angles of quardrilateral are 4x,5(x+2)°,(7x-20)° and 6(x+3)°.find: (a) the value of x (b) each angle of the quardrilateral ​

Answer 1

Angles of the quadrilateral are 4x, 5(x+2)°,(7x-20)° and 6(x+3)°

(a) According to the angle sum property, the angles of a quadrilateral sum up to 360°.

Thus,

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

$\implies$4x + 5x + 10 + 7x - 20 + 6x + 18 = 360°

$\implies$22x + 8 = 360°

$\implies$22x = 352°

$\implies$x = 16°

(b) Hence the 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°

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