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. What is the missing step

Question

Mathematics

Alayna Cannon

21 July, 07:43

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. What is the missing step

+3

Answers (1)

Know the Answer?

Tate · Answer 1

the [Missing Step]

according to the figure, ∠OCP and ∠ABC are congruent, these angles are called corresponding angles. By the definition of congruent angles, m∠OCP = m∠ABC