Chapter 3.3, Problem 8PSA

To determine

To find the value of x, y and z.

Answer to Problem 8PSA

  $Thevalueof x=5/3,y=100andz= 8100.$

Explanation of Solution

Given information:

  $\Delta ABC \cong \Delta DEF$

  $\angle A=90°,\angle B=50°and\angle C=40°.$

  $m\angle E=12x+30,$

  $m\angle F=y/2–10,$

  $m\angle D=\surd z$

Formula used:

As corresponding parts of congruent triangles are congruent,

  $\begin{array}{l}\angle E\cong \angle B\hfill \\ \angle F\cong \angle C\hfill \\ \angle D\cong \angle A\hfill \end{array}$

Calculation:

  

  $\angle E\cong \angle B$

  $\begin{array}{l}12x+30=50\hfill \\ \therefore 12x=20\hfill \\ \therefore x=20/12=5/3\hfill \end{array}$

  $\angle F\cong \angle C$

  $\begin{array}{l}y/2–10=40\hfill \\ \therefore y/2=50\hfill \\ \therefore y=100\hfill \end{array}$

  $\angle D\cong \angle A$

  $\begin{array}{l}\surd z=90\hfill \\ \therefore z=8100\hfill \end{array}$