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I need help with this because my teacher hasn't taught me this.

I need help with this because my teacher hasn't taught me this.-example-1

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\begin{gathered} \angle1=\angle4=30^(\circ)\Rightarrow Verticle\text{ angle} \\ Now, \\ \angle6+\angle7=180 \\ 35+\angle7=180 \\ \angle7=145^(\circ)\Rightarrow Angle\text{ on a straight line} \\ \text{Now,} \\ \angle8=\angle6=35^(\circ)\Rightarrow verticle\text{ angle} \\ \text{Now,} \\ \angle5=\angle4=30^(\circ)\Rightarrow Alternate\text{ exterior angle} \end{gathered}

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