Chapter 12.2, Problem 24E

To determine

To find:

Thevalues of $x$ and $y$ .

Answer to Problem 24E

  $x=5$

  $y=2$ .

Explanation of Solution

Given:

  $\Delta STU\cong \Delta XYZ$

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

  $\begin{array}{l}m\angle T=m\angle Y\\ 28=8x-6y\\ m\angle Z=180-130-8x+6y\\ m\angle Z=m\angle U\\ 50-8x+6y=4x+y\\ 50=12x-5y\\ 28=8x-6y\\ 300=72x-30y\\ -140=-40x+30y\\ x=5,y=2\end{array}$

The pairs of congruent corresponding sides

Therefore,

The values of $x=5$ and $y=2$ .

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