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

Ray KM is an angle bisector of .

Step-by-step explanation:

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

Angle between KJ and KN is i.e.

Angle between KN and KM is i.e.  .

Angle between KM and KL is i.e.  

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.

and

So, it is also incorrect.

3. Ray KM is an angle bisector of .

Ray KM divides the into two equal angles and so it is correct.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180