Option C:
∠BPD congruent to ∠APC.
Solution:
To find which statement is true about ∠BPD.
Option A: It is adjacent to ∠APC.
∠BPD adjacent to ∠APD and ∠BPC.
So, it is not adjacent to ∠APC.
Hence it is false statement.
Option B: It is complementary to ∠BPC.
In a straight line adjacent angles are supplementary.
In straight line CD, ∠BPC + ∠BPD = 180°.
So, ∠BPD is supplementary to ∠BPC.
Hence it is false statement.
Option C: It is congruent to ∠APC.
∠APC and ∠BPD are vertically opposite angles.
If two lines are intersect, then vertically opposite angles are congruent.
So, ∠BPD ≅ ∠APC.
Hence it is true statement.
Option D: It is linear to ∠APC.
∠APC and ∠BPD are not adjacent angles.
So they did not form a linear pair.
Hence it is false statement.
Therefore, option C is the correct answer.
∠BPD congruent to ∠APC.
