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State whether the statement is true or false.

$∠ 4$ and $∠ 5$ are alternate angles.

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True

False

answer is A.

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Detailed Solution

Given that:
Question Image

We need to verify whether

∠ 4

and

∠ 5

are alternate angles.
The angles that are in opposite sides of the traversal line and with same angle is called as alternate angle.
From the given figure,

∠ 5

and

∠ 7

are vertically opposite angles.
The alternate angle is

∠ 6 = 55^{\circ}

The adjacent angles on straight line is,

\Rightarrow ∠ 7 + ∠ 6 = 180^{\circ}

\Rightarrow ∠ 7 + 55^{\circ} = 180^{\circ}

\Rightarrow ∠ 7 = 125^{\circ}

∠ 1

and

∠ 8

are not corresponding angles.
Hence,

∠ 4

and

∠ 5

are alternate angles.
Therefore, option 1 is correct.

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