Question

The figure shows a parallelogram ABCD where ADC = 108". E lies on AB such
that BĈE = 38"
108"
В
0 Given that ABC =9x", find the value of x.
(ii) Find DĈE.
the value of x and of y.​

Answer 1

Answer:

let the angle DCE be x ,

so as we know that Angle D + Angle C = 180

then, 108+38+x =180

146+x=180

x=34 .

Answer 2

Given : The figure shows a parallelogram ABCD where ADC = 108". E lies on AB such  that BĈE = 38° . ABC =9x

To find : the value of x and ∠DĈE.

Solution:

Opposite angles in parallelogram are equal

Hence

∠ABC =  ∠ADC

∠ADC= 108°   given

=> ∠ABC = 108°

∠ABC = 9x

Equating both

9x = 108

=> x = 12

Adjacent angles in parallelogram adds upto 180°

=> ∠ADC + ∠DCB = 180°

=> 108° + ∠DCB = 180°

=> ∠DCB =74°

∠DCB  = ∠DCE +  ∠BCE

=> 74° = ∠DCE + 38°

=> ∠DCE  = 36°

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