Chapter 6.2, Problem 2ACYP

To determine

To calculate: To find the value of each variable in the given parallelogram.

Answer to Problem 2ACYP

The values of variables are $x^{\circ }={31}^{\circ }$ and $y=2$ .

Explanation of Solution

Given: Parallelogram is

  

Formula Used:

In a parallelogram,

• Opposite sides are equal
• Consecutive angles are supplementary

Calculation:

Parallelogram is given as

  

Since opposite sides of parallelogram are equal,

Thus, $y+8=5y$

Solving the above equation:

  $\begin{array}{l}5y-y=8\\ 4y=8\\ y=2\end{array}$

Also, consecutive sides of parallelogram are supplementary,

Thus, $4x^{\circ }+{\left(2x-6\right)}^{\circ }={180}^{\circ }$

On solving the above equation:

  $\begin{array}{l}4x^{\circ }+2x^{\circ }={180}^{\circ }+6^{\circ }\\ 6x^{\circ }={186}^{\circ }\\ x^{\circ }={31}^{\circ }\end{array}$

Conclusion:

Hence, Value of variables are $x^{\circ }={31}^{\circ }$ and $y=2$ .