Chapter 6.3, Problem 5CYU

To determine

To find: The value of $\mathrm{x}$ and $\mathrm{y}$ .

Answer to Problem 5CYU

The value of $\mathrm{x}$ and $\mathrm{y}$ are $4$ and $5$ respectively.

Explanation of Solution

Given information:

The given figure is,

  

Concept used:

The condition satisfied by the quadrilateral are,

• Both pairs of the opposite sides are parallel
• Both pairs of the opposite sides are congruent
• One pair of opposite sides are congruent
• Diagonals bisect each other

The value of $\mathrm{x}$ is calculated as,

  $\begin{array}{l}2\mathrm{x}+3=\mathrm{x}+7\\ 2\mathrm{x}-\mathrm{x}=7-3\\ \mathrm{x}=4\end{array}$

The value of $\mathrm{y}$ is calculated as,

  $\begin{array}{l}3\mathrm{y}-5=\mathrm{y}+5\\ 3\mathrm{y}-\mathrm{y}=5+5\\ \mathrm{y}=5\end{array}$

Thus, the value of $\mathrm{x}$ and $\mathrm{y}$ are $4$ and $5$ respectively.