Question

given: ∠jlm ≅ ∠klm
prove: m∠jlm = 90°
by the linear pair theorem, ∠jlm is supplementary to ∠klm. since ∠jlm ≅ ∠klm, by the definition of congruence, m∠jlm = m∠klm. applying the substitution property of equality, m∠jlm + m∠jlm = 180°. simplifying the equation, m∠jlm = 90°.
what step is missing from this proof?
a. ∠jlm ≅ ∠klm by the linear pair theorem.
b. m∠jlm = m∠klm by the definition of congruence.
c. m∠jlm + m∠klm = 180° by the definition of supplementary angles.
d. ∠jlm is supplementary to ∠klm by the transitive property.

Explanation:

We know that supplementary angles add up to 180°. Since ∠JLM and ∠KLM are supplementary (by the linear - pair theorem), the step that should be explicitly stated before substituting m∠KLM with m∠JLM is that m∠JLM + m∠KLM=180° based on the definition of supplementary angles.

Answer:

C. m∠JLM + m∠KLM = 180° by the definition of supplementary angles.