Question

ABCD IS A PARRLELOGRAM . FIND X

Answer 1

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Class 8

>>Maths

>>Understanding Quadrilaterals

>>Parallelogram

>>In the following figure, ABCD is a paral

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In the following figure, ABCD is a parallelogram. Find the value of x

182370

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Solution

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Correct option is B)

GiventhatABCDisaparallelogram.

Weknowthatinaparallelogramoppositeanglesareequal.

Sofromthegivenfigure,

∠B=∠D⇒6x+3y−8=7y⇒6x−4y=8⇒x=

6

8+4y

−−−−(1)

Alsoweknowthatadjacentanglesinaparallelogramaresupplementary.

So∠A+∠D=180

o

⇒4x+20+6x+3y−8=180

o

⇒10x+3y=168−−−−(2)

Using1in2,

10(

6

8+4y

)+3y=168⇒80+40y+18y=168×6⇒58y=1008−80⇒58y=928⇒y=

58

928

⇒y=16

o

Usingy=16in1,

x=

6

8+4×16

⇒x=

6

8+64

⇒x=

6

72

⇒x=12

o

Sox=12

o

&y=16

o