Question

select the correct answer.
given: $\angle jlm \cong \angle klm$
prove: $m\angle jlm = 90^\circ$
image of a diagram with points j, l, k vertically aligned and m horizontally left from l
by the linear pair theorem, $\angle jlm$ is supplementary to $\angle klm$. since $\angle jlm \cong \angle klm$, by the definition of congruence, $m\angle jlm = m\angle klm$. applying the substitution property of equality, $m\angle jlm + m\angle jlm = 180^\circ$. simplifying the equation, $m\angle jlm = 90^\circ$.
what step is missing from this proof?
a. $m\angle jlm = m\angle klm$ by the definition of congruence.
b. $\angle jlm \cong \angle klm$ by the linear pair theorem.
c. $m\angle jlm + m\angle klm = 180^\circ$ by the definition of supplementary angles.
d. $\angle jlm$ is supplementary to $\angle klm$ by the transitive property.

Explanation:

The proof states ∠JLM and ∠KLM are supplementary via the linear pair theorem, but it skips explicitly stating that supplementary angles have a sum of 180°. Option A is already mentioned, Option B is incorrect (linear pair theorem does not prove congruence), Option D is wrong (transitive property does not apply here). Option C fills the gap by connecting the supplementary angle statement to their measure sum.

Answer:

C. $\text{m}\angle JLM + \text{m}\angle KLM = 180^\circ$ by the definition of supplementary angles.