Chapter 6.1, Problem 20CE

To determine

The reasons to complete proof $m\angle 2>m\angle 4$ .

Answer to Problem 20CE

  $m\angle 2>m\angle 4$

Explanation of Solution

Given:

The diagram is shown below:

  

  $m\angle 2>m\angle 1$

Calculation:

Proof with the reasons is given below:

  $\begin{array}{l}m\angle 2>m\angle 1\mathrm{......}\left(1\right)\left(\text{Given}\right)\\ m\angle 1>m\angle 3\left(\begin{array}{l}\text{Exterior angle is greater than any}\\ \text{interior angle of triangle}\end{array}\right)\\ m\angle 2>m\angle 3\mathrm{......}\left(2\right)\left(\text{From equation }\left(1\right)\right)\\ m\angle 3=m\angle 4\left(\text{Vertical opposite angle}\right)\\ m\angle 2>m\angle 4\left(\text{From equation }\left(2\right)\right)\end{array}$

Hence,

  $m\angle 2>m\angle 4$