Question

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In Quadrilateral ABCD, ∠A = 66, ∠B = ∠C + 16; ∠C = 6(x+4) and ∠D = (∠A -16). Find the value of x.

Answer 1

Answer

Given,

In quadrilateral ABCD

angle A=66 degree

angle B=∠C + 16

            =6[x+4]+16

             =6x+24+16

              =6x+40 degrees

∠C =6[x+4]

      =6x+24degrees

∠D=[∠A-16]

    =[66-16]

    =50 degrees

thus In quadrilateral ABCD by angle sum property

∠A+∠B+∠C+∠D=360 degree   [sum of all angles in a quadrilateral is 360 degree]

66+6x+40+6x+24+50=360 degree

180+12x=360 degree

12x=360-180

x=180/12

x=15 degree

Thus value of x is 15 degrees.