Question

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

Explanation:

Step1: Analyze the given information

We are given \(m\angle MXY = m\angle KXY\) (given) and \(m\angle JXM=m\angle NXK\) (vertical angles theorem).

Step2: Use the angle addition postulate

The angle addition postulate states that if we have two adjacent angles, the measure of the larger angle is the sum of the measures of the smaller angles.
We know that \(m\angle JXY=m\angle JXM + m\angle MXY\) and \(m\angle NXY=m\angle NXK + m\angle KXY\).
Since \(m\angle MXY = m\angle KXY\) and \(m\angle JXM=m\angle NXK\), by substitution, \(m\angle JXY=m\angle NXY\).

Answer:

C. \(m\angle JXY = m\angle NXY\)