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katrin2010 [14]
3 years ago
9

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

Mathematics
1 answer:
n200080 [17]3 years ago
7 0
<h2>x^{\circ}=21^{\circ} \ and \ y^{\circ}=39^{\circ}</h2>

Step-by-step explanation:

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

\angle ABC =\angle ADC\ and \ \angle BAD = \angle DAC

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

⇒3x^{\circ}-4x^{\circ}=-21^{\circ} \ and \ 3y^{\circ}-y^{\circ}=78^{\circ}

⇒-x^{\circ}=-21^{\circ} \ and \ 2y^{\circ}=78^{\circ}

⇒x^{\circ}=21^{\circ} \ and \ y^{\circ}=39^{\circ}

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