Question

In the adjacent diagram if x:y=3:4 and y:z=1:2 then find angle DCB.

Answer 1

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Answer:-

x=36° and y=48° and z=96°

Step-by-step explanation:-

Given: x:y=3:4 and y:z=1:2

To find: Measure of ∠DCB

Solution:x:y=3:4   [GIVEN]

Which means,   x = 3

                          y    4

Now cross multiplying,we get,

4x=3y

4x =y      ----(1 st equation)

 3

Now we put value of y in y:z=1:2,

y:z=1:2

Which means, y = 1

                        z    2

Now cross multiplication,

2y=z

Now we put value of y from 1st equation,

2× 4x =z

     3

∴z= 8x    ----(2nd equation)

       3

Now,x+y+z=180°    [Angle sum property]

Putting values of y and z from equation 1 and 2

x+ 4x + 8x =180°

     3       3

3x + 4x + 8x =180°

         3

15x =180°

  3

15x=540°

∴x=540°/15 =36°

Hence,x=36°

y=4x/3=4×36/3=48°

z=8x/3=8×36/3=96°

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