Question

Quadrilateral ABCD is a rhombus. If mzCDB = 6y° and mZACB = (2y + 10)°, find the value of y.

Answer 1

Answer:
`y=10`

Explanation:

Note that
`\angle ACB \cong \angle ACD` because diagonals of a rhombus bisect the angles from which they are drawn.

Now, because
`m\angle DEC=90^(\circ)` since diagonals of a rhombus are perpendicular, it follows that
`m\angle CDB+m\angle ABC=90^(\circ)`.

`6y+2y+10=90\\\\8y+10=90\\\\8y=80\\\\y=10`