Chapter 12.2, Problem 10E

To determine

To find:

Thevalues of $x$ and $y$ .

Answer to Problem 10E

  $x=32$

  $y=51$ .

Explanation of Solution

Given:

  $\Delta MNP\cong \Delta TUS$

Concept used:

Two geometric figures are congruent if a rigid motion or a composition of rigid motions maps one of the figures onto other.

Calculation:

The pairs of congruent corresponding angles

  $\begin{array}{l}m\angle N=m\angle U\\ {180}^0-{142}^0-{24}^0={\left(2x-50\right)}^0\\ 14=2x-50\\ 64=2x\\ 32=x\end{array}$

The pairs of congruent corresponding sides

  $\begin{array}{l}NP=US\\ 2x-y=13\\ 2\left(32\right)-y=13\\ 64-y=13\\ -y=-51\\ y=51\end{array}$

Therefore,

The values of $x=32$ and $y=51$ .