Chapter 1.6, Problem 11PSC

a.

To determine

To Prove: $m\angle 1=m\angle J+m\angle H$

Explanation of Solution

Given:

  

  $m\angle J+m\angle H+m\angle JKH=180°$

Concept Used:

Exterior angle is equal to sum of interior opposite angles. Sum of linear pair of angles is $180°$

Proof:

Here, we have

  $m\angle J+m\angle H+m\angle JKH=180°$

Since, sum of linear pair of angles is $180°$ .

  $\begin{array}{l}\angle JKH+\angle 1=180°\\ \Rightarrow m\angle J+m\angle H+m\angle JKH=m\angle JKH+m\angle 1\\ \Rightarrow m\angle J+m\angle H=m\angle 1\\ \therefore m\angle 1=m\angle J+m\angle H\end{array}$

Thus, exterior angle is equal to sum of interior opposite angles.

b.

To determine

To Prove: $m\angle 1>m\angle J$

Explanation of Solution

Given:

  

  $m\angle J+m\angle H+m\angle JKH=180°$

Concept Used:

Exterior angle is equal to sum of interior opposite angles. Sum of linear pair of angles is $180°$

Proof:

Here, we have

  $m\angle J+m\angle H+m\angle JKH=180°$

Since, sum of linear pair of angles is $180°$ .

  $\begin{array}{l}\angle JKH+\angle 1=180°\\ \Rightarrow m\angle J+m\angle H+m\angle JKH=m\angle JKH+m\angle 1\\ \Rightarrow m\angle J+m\angle H=m\angle 1\\ \Rightarrow m\angle 1>m\angle J\end{array}$