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Mathematics, 11.11.2020 01:00 mariaaalopezz

Given: , , and . Prove: ∠PCQ is complementary to ∠ABC. Proof: Since , m∠OCQ = 90° by the definition of perpendicular lines. By angle addition, we can say m∠OCQ = m∠OCP + m∠PCQ. But since m∠OCQ = 90°, m∠OCP + m∠PCQ = 90° by the Transitive Property of Equality. [Missing Step] By the definition of congruent angles, m∠OCP = m∠ABC. This leads to m∠ABC + m∠PCQ = 90° by the Transitive Property of Equality. So, based on the definition of complementary angles, ∠PCQ is complementary to ∠ABC. 35 What is the missing step in the given proof? A. ∠PQC 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.

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Given: , , and . Prove: ∠PCQ is complementary to ∠ABC. Proof: Since , m∠OCQ = 90° by the definition...
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