Mathematics: Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees. Which statement must be true about the diagram? Point K is a midpoint of Line segment J L. mAngleJKN = One-halfmAngleJKM Ray KM is an angle bisector of AngleNKL. JK = One-halfKL

Four lines extend from point K. The space between

nidiavega2009

29.01.2022

Ray KM is an angle bisector of $\angle NKL$ .

Step-by-step explanation:

Given that there are 4 lines that are extended from a point K.

Angle between KJ and KN is $58^\circ$ i.e. $\angle JKN =$ $58^\circ$

Angle between KN and KM is $61^\circ$ i.e. $\angle NKM =$ $61^\circ$ .

Angle between KM and KL is $61^\circ$ i.e. $\angle MKL =$ $61^\circ$

Please refer to the attached image for the conditions and dimensions of angles given in the question statement.

Now, let us have a look at the options given:

1. Point K is a midpoint of Line segment JL

JL is not a straight line first of all, and secondly there is no condition given about the line segments.

So, it is incorrect.

2. $m \angle JKN = \dfrac{1}{2}m \angle JKM$

$\angle JKN =$ $58^\circ$ and

$m \angle JKM =58+61=139^\circ\\\Rightarrow \dfrac{1}{2} m \angle JKM = 64.5^\circ$

So, it is also incorrect.

3. Ray KM is an angle bisector of $\angle NKL$ .

Ray KM divides the $\angle NKL$ into two equal angles $\angle NKM =$ $61^\circ$ and $\angle MKL =$ $61^\circ$ so it is correct.

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