Question: prove pcq is complementary to abc?
Answer: Given: AC||BD , AB||CD, and AC _|_ CD Prove: ∠PCQ is complementary to ∠ABC. Proof: Since AC _|_ CD m∠OCQ = 90° by the definition of perpendicular lines. By angle addition, we can say m∠OCQ = m∠OCP + m∠PCQ. ... ∠PQC and ∠ACP are supplementary by the Linear Pair Theorem.