Question

select the correct answer.
given: ( mangle mxy = mangle kxy )
what is the conclusion reached by this proof?
a. ( mangle jxm = mangle nxk )
b. ( mangle mxy = mangle kxy )
c. ( mangle jxy = mangle nxy )
d. ( mangle jxn = mangle mxk )

Explanation:

The proof uses the given \( m\angle MXY = m\angle KXY \) and the vertical angles theorem (\( m\angle JXM = m\angle NXK \)) with the angle addition postulate to conclude \( m\angle JXY = m\angle NXY \). Options A and B are given (not the conclusion), and D is not derived here. So the conclusion is \( m\angle JXY = m\angle NXY \).

Answer:

C. \( \boldsymbol{m\angle JXY = m\angle NXY} \)