Question

Find the values of the variables in eachparallelogram. Write the equations andsolve showing ALL the work.

Answer 1

Given

parallelogram

Procedure

Properties of parallelograms

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The diagonals of a parallelogram bisect each other.

Each diagonal of a parallelogram separates it into two congruent triangles.

Solving for x

`\begin{gathered} 3x+1=5x-1 \\ 5x-3x=2 \\ 2x=2 \\ x=1 \end{gathered}`

Now for y

`\begin{gathered} 2y-9=y-2 \\ 2y-y=9-2 \\ y=7 \end{gathered}`