Question

For what value of “x” is the figure the given special parallelogram?

Answer 1

x = 6

Explanation:

(In reference to my diagram.... my diagram is similar to the diagram in the question)

We know that diagonals of a square bisect each other at right angles.

In ΔBOC ,

•OB = OC (Diagonals of square bisect each other)

=> ∠OBC = ∠OCB = (7x + 3)° (∵ OB = OC)

• ∠BOC = 90° (Diagonals intersect at right angles)

Using angle sum property of triangle ,

∠OBC + ∠OCB + ∠BOC = 90°

`= > 7x + 3 + 7x + 3 + 90 = 180`

`= > 14x + 6 = 180 - 90 = 90`

`= > 14x = 90 - 6 = 84`

`= > x = (84)/(14) = 6`