Option a is the correct answer.
Solution:
Option a:
Step 1: Given [tex]l \| m[/tex]
line l and m are parallel lines.
Step 2: ∠p and ∠d are vertically opposite angles.
Vertical angle theorem:
If two angles are vertically opposite then the two angles are congruent.
∠p ≅ ∠d by vertical angle theorem.
Step 3: ∠d and ∠c are same side interior angles.
we know that, interior angles in the same side are supplementary.
So, ∠d and ∠c are supplementary.
Step 4: ∠c and ∠k are vertically opposite angles.
∠c ≅ ∠k by vertical angle theorem.
Step 5: By step 2 and step 3,
∠p and ∠c are supplementary.
Substitute step 4, we get
∠p and ∠k are supplementary.
Hence it is true.
Option b:
Step 1: Given [tex]l \| m[/tex]
line l and m are parallel lines.
Step 2: ∠p ≅ ∠k by corresponding angles is given.
∠p and ∠h are the corresponding angles.
∠p and ∠k are not corresponding angles.
From step 2 on wards it is not true. so need not to verify the other steps.
Hence it is false.
