Question

GK∥HJ. Complete the proof that m∠IHK=m∠G+m∠K without using the Triangle Angle Sum Theorem.GKHIJ

Answer 1

Explanation

We are given the following:

`GK||HJ`

We are required to prove that:

`m\angle IHK=m\angle G+m\angle K`

We already know that:

`\begin{gathered} GK||HJ\text{ \textbraceleft Given\textbraceright} \\ \\ \angle G\cong\angle IHJ\text{ \textbraceleft Corresponding Angles Theorem\textbraceright} \end{gathered}`

Now, we have:

`\angle K\cong\angle JHK\text{ \textbraceleft Alternate Interior Angles Theorem\textbraceright}`

Also, we have: