Question

What is the conclusion reached by this proof?A. B. C. D.

Answer 1

We are given that the measure of the following angles is the same:

$m\angle MXY=m\angle KXY$

And, by the vertical angles theorem we know that:

$m\angle JXM=m\angle NXK$

Now, the "Angle Addition Postulate" states that the measure of an angle is equal to the sum of the measure of smaller angles in between.

Applying the postulate to angle MXY we get:

$m\angle NXY=m\angle NXK+m\angle\text{KXY}$

And, applying the postulate to angle JXY we get:

$m\angle JXY=m\angle JXM+m\angle\text{MXY}$

Now, we subtract the equations, we get:

$m\angle NXY-m\angle JXY=m\angle NXK+m\angle\text{KXY-}m\angle JXM-m\angle\text{MXY}$

From the initial statement, we can cancel out the measure of angles KXY and MXY since they are equal:

$m\angle NXY-m\angle JXY=m\angle NXK\text{-}m\angle JXM$

Also, from the vertical angles theorem we can cancel out the measure of angles NXK and JXM:

$m\angle NXY-m\angle JXY=0$

Now, we add the measure of angle JXY:

$m\angle NXY=m\angle JXY$

Therefore, the conclusion is option D.