Question

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

Answer 1

`x^(\circ)=21^(\circ) \ and \ y^(\circ)=39^(\circ)`

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)`