Chapter 1.6, Problem 2PSA

To determine

To Prove: $\angle FEH\cong \angle JKM$

Explanation of Solution

Given:

  

Concept Used:

Sum of linear pair of angles is $180°$

Proof:

Here, we have

  $\begin{array}{l}\Rightarrow m\angle DEF=x°,m\angle FEH=\left(3x\right)°\\ \text{Since sum of linear pair of angles is }180°\\ \Rightarrow \angle DEF+\angle FEH=180°\\ \Rightarrow x°+\left(3x\right)°=180°\\ \Rightarrow \left(4x\right)°=180°\\ \Rightarrow x=45\\ \Rightarrow m\angle DEF=45°,\\ m\angle FEH=\left(3\times 45\right)°=135°\\ \text{Also }m\angle JKM=135°\\ \Rightarrow \angle FEH\cong \angle JKM\end{array}$