Question

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

Answer 1

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

Step-by-step explanation:

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

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

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

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

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

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