Chapter 4.1, Problem 7WE

To determine

ToName : Name the four congruent angles from the given informations.

Answer to Problem 7WE

The final answer is $m\angle R=100,m\angle E=40,m\angle S=40andm\angle T=40$

Explanation of Solution

Given information : We have given that $\Delta DEF\cong \Delta RST$ , $m\angle D=100$ and $m\angle F=40$

In $\Delta DEF$

  $m\angle D=100$ and $m\angle F=40$

Therefore, from angle sum property we have

  $\begin{array}{c}m\angle E=180-\left(100+40\right)\\ =180-140\\ =40\end{array}$

Since $\Delta DEF\cong \Delta RST$

For the congruent triangles their corresponding sides and angles are equal.

So we must have

  $D\leftrightarrow R$ , $E\leftrightarrow S$ , $F\leftrightarrow T$

Therefore, the four congruent angles are

  $m\angle R=100,m\angle E=40,m\angle S=40andm\angle T=40$