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

GKHJ Complete The Proof That MIHKmGmK Without Using The Triangle Angle Sum TheoremGKHIJ class=
GKHJ Complete The Proof That MIHKmGmK Without Using The Triangle Angle Sum TheoremGKHIJ class=
GKHJ Complete The Proof That MIHKmGmK Without Using The Triangle Angle Sum TheoremGKHIJ class=

Answer :

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]

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