Statement
$∠ 1$ is supplement to $∠ 8$ .

Provide appropriate reason for the same if $l$ is parallel to $m$ and a transversal intersects these parallel lines.

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Solution

Reason $:$
$∠ 1 = ∠ 5$ (Corresponding angles as $l | | m$ )
$∠ 5 + ∠ 8 = 180^{\circ}$ (Supplementary angles made on a line made at a point)
Put $∠ 5 = ∠ 1$
$∠ 1 + ∠ 8 = 180^{\circ}$
So $∠ 1$ is supplement to $∠ 8$

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Which of the following statements are true (I) and which are false (F)? Give reasons.
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(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
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Fill in the blanks in each of the following to make the statement true:
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Statement ∠1 is supplement to ∠8 .Provide appropriate reason for the same if l is parallel to m and a transversal intersects these parallel lines.

Reason :∠1=∠5 (Corresponding angles as l||m)∠5+∠8=180∘ (Supplementary angles made on a line made at a point)Put ∠5=∠1∠1+∠8=180∘So ∠1 is supplement to ∠8

Statement
$∠ 1$ is supplement to $∠ 8$ .

Provide appropriate reason for the same if $l$ is parallel to $m$ and a transversal intersects these parallel lines.

Reason $:$
$∠ 1 = ∠ 5$ (Corresponding angles as $l | | m$ )
$∠ 5 + ∠ 8 = 180^{\circ}$ (Supplementary angles made on a line made at a point)
Put $∠ 5 = ∠ 1$
$∠ 1 + ∠ 8 = 180^{\circ}$
So $∠ 1$ is supplement to $∠ 8$