What is the missing step in the given proof?

A) PCQ and ACP are supplementary by the Linear Pair Theorem.
B) For parallel lines cut by a transversal, corresponding angles are congruent, so ACB PCQ.
C) OCP BCD by the Vertical Angles Theorem.
D) For parallel lines cut by a transversal, corresponding angles are congruent, so OCP ABC.
E)For parallel lines cut by a transversal, corresponding angles are congruent, so OCA CBD.

Question

What is the missing step in the given proof?

A) PCQ and   ACP are supplementary by the Linear Pair Theorem.
B) For parallel lines cut by a transversal, corresponding angles are congruent, so  ACB    PCQ.
C) OCP    BCD by the Vertical Angles Theorem.
D) For parallel lines cut by a transversal, corresponding angles are congruent, so OCP    ABC.
E)For parallel lines cut by a transversal, corresponding angles are congruent, so OCA    CBD.

anonymous · Answer

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anonymous · Answer

Proof: Since       , mOCQ = 90° by the definition of perpendicular lines. By angle addition, we can say mOCQ = mOCP + mPCQ. But since mOCQ = 90°, mOCP + mPCQ = 90° by the Transitive Property of Equality. 

[Missing Step]

By the definition of congruent angles, mOCP = mABC. This leads to 
mABC + mPCQ = 90° by the Transitive Property of Equality. So, based on the definition of complementary angles, PCQ is complementary to ABC.