Mathematics

Based on the given figure, which of the following statements is true?


ANSWER

$$\angle\, 4$$ and $$\angle\, 5$$ are alternate angles.


SOLUTION
$$\angle 5$$ and $$\angle 7$$ are vertically opposite angles.
$$\angle 6=55^{\circ}$$      (Alternate angles)
$$\angle 7+\angle 6=180^{\circ}$$  (Adjacent angle on straight line)
$$\Rightarrow \angle 7+{ 55 }^{ \circ  }={ 180 }^{ \circ  }\\ \Rightarrow \angle 7={ 125 }^{ \circ  }$$
$$\angle 1$$ and $$\angle 8$$ are not corresponding angles.
$$\angle 4$$ and $$\angle 5$$ are alternate angles.
So only option $$D$$ is correct.
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