Question

1.6.4 test (cst): post test: foundations of geometry
m∠mxy = m∠kxy
given
m∠jxm = m∠nxk
vertical angles theorem
m∠jxy = m∠nxy
angle addition postulate
what is the conclusion reached by this proof?
a. m∠jxy = m∠nxy
b. m∠mxy = m∠kxy
c. m∠jxm = m∠nxk
d. ...

Explanation:

Step1: Identify given premises

We start with two given/derived premises:

1. $m\angle MXY = m\angle KXY$ (given)
2. $m\angle JXM = m\angle NXK$ (from vertical angles theorem)

Step2: Apply angle addition postulate

The angle addition postulate combines these pairs:
$m\angle JXY = m\angle JXM + m\angle MXY$
$m\angle NXY = m\angle NXK + m\angle KXY$
Substituting the equal angle measures from Step1, we get $m\angle JXY = m\angle NXY$, which is the final result of the proof chain.

Step3: Match to the conclusion

The statement $m\angle JXY = m\angle NXY$ is the end product of the proof, so it is the conclusion.

Answer:

A. $m\angle JXY = m\angle NXY$