Question

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

Answer 1

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

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 = (1)/(2)m \angle JKM`

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

`m \angle JKM =58+61=139^\circ\\\Rightarrow (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.