Chapter 6.1, Problem 11WE

To determine

To Prove: $m\angle 1>m\angle 4$ in two-column form shown in figure.

Explanation of Solution

Given Figure is shown as.

  

Calculation:

Since, $\angle$ is exterior angle of the triangle, therefore.

  $\begin{array}{cc}\text{Statements}& \text{Reasons}\\ \begin{array}{l}m\angle 1>m\angle 2\\ m\angle 2>m\angle 3\end{array}& \text{Using Exterior angle Inequality Theorem}\\ m\angle 1>m\angle 3& \text{If a>b and b>c, then a>c}\\ m\angle 3=m\angle 4& \text{Vertically Opposite angles}\\ m\angle 1>m\angle 4& \text{Substitution Property}\end{array}$

Therefore, it has been proved.