Chapter 3, Problem 8RP

To determine

To calculate: The values of x, y and z

Answer to Problem 8RP

Values of x, y and z are $30°,120°$ and $30°$ respectively.

Explanation of Solution

Given information : Here, we have given that $\Delta RST\cong \Delta DFE$ , $\angle R=50°$ , $\angle T=40°$ , $\angle S=90°$ , $\angle D=(x+20)°$ , $\angle E=(y+10)°$ and $\angle F=(z-30)°$ .

Formula used : Congruent parts of congruent triangles are equal.

Calculation: As, $\Delta RST\cong \Delta DFE$ ,

  $\begin{array}{l}\Rightarrow \angle R=\angle D\\ \Rightarrow 50°=(x+20)°\\ \Rightarrow x°=(50-20)°\\ \Rightarrow x°=30°\end{array}$

Similarly,

  $\begin{array}{l}\Rightarrow \angle S=\angle F\\ \Rightarrow 90°=(z-30)°\\ \Rightarrow z°=(90+30)°\\ \Rightarrow z°=120°\end{array}$

Similarly,

  $\begin{array}{l}\Rightarrow \angle T=\angle E\\ \Rightarrow 40°=(y+10)°\\ \Rightarrow y°=(40-10)°\\ \Rightarrow y°=30°\end{array}$