Explanation
We are given the following:
[tex]GK||HJ[/tex]
We are required to prove that:
[tex]m\angle IHK=m\angle G+m\angle K[/tex]
We already know that:
[tex]\begin{gathered} GK||HJ\text{ \textbraceleft Given\textbraceright} \\ \\ \angle G\cong\angle IHJ\text{ \textbraceleft Corresponding Angles Theorem\textbraceright} \end{gathered}[/tex]
Now, we have:
[tex]\angle K\cong\angle JHK\text{ \textbraceleft Alternate Interior Angles Theorem\textbraceright}[/tex]
Also, we have:
[tex]m\angle IHK=m\operatorname{\angle}IHJ+m\operatorname{\angle}JHK\text{ \textbraceleft Additive Property of Angle Measure\textbraceright}[/tex]
