i need help please !
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Answer:
See Explanation
Step-by-step explanation:
[tex] \overrightarrow{KH} \: bisects \: \angle GKJ[/tex] (Given)
[tex] \therefore \angle GKH \cong \angle HKJ[/tex] (angle bisector theorem)
[tex] \therefore m\angle GKH = m\angle HKJ[/tex]
[tex] \implies m \angle 11 =m \angle 12[/tex]
[tex] m\angle 9 + m\angle 12 = 180\degree.... (1)[/tex](Linear pair angles)
&
[tex] m\angle 10 + m\angle 11 = 180\degree[/tex](Linear pair angles)
[tex]\implies m\angle 10 + m\angle 12 = 180\degree.... (2)[/tex] [tex] (\because m \angle 11 = m\angle 12)[/tex]
From equations (1) & (2)
[tex] m\angle 9 + \cancel {m\angle 12} =m\angle 10 + \cancel {m\angle 12}[/tex]
[tex]\therefore m\angle 9 =m\angle 10 [/tex]
[tex]\implies \huge \orange {\angle 9 \cong \angle 10} [/tex]
Thus proved