lovehr148
lovehr148 lovehr148
  • 24-01-2020
  • Mathematics
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For what values of x and y must ABCD be a parallelogram?

For what values of x and y must ABCD be a parallelogram class=

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DevonFen DevonFen
  • 01-02-2020

[tex]x^{\circ}=21^{\circ} \ and \ y^{\circ}=39^{\circ}[/tex]

Step-by-step explanation:

We know that vertically opposite angles of a parallelogram are equal .

[tex]\angle ABC =\angle ADC\ and \ \angle BAD = \angle DAC[/tex]

⇒[tex]3x^{\circ}=(4x-21)^{\circ} \ and \ 3y^{\circ}=(y+78)^{\circ}[/tex]

⇒[tex]3x^{\circ}-4x^{\circ}=-21^{\circ} \ and \ 3y^{\circ}-y^{\circ}=78^{\circ}[/tex]

⇒[tex]-x^{\circ}=-21^{\circ} \ and \ 2y^{\circ}=78^{\circ}[/tex]

⇒[tex]x^{\circ}=21^{\circ} \ and \ y^{\circ}=39^{\circ}[/tex]

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