Question

MO bisects angle LMO = 6x-22, and angle NMO = 2x + 34. solve for x and find angle LMN.

Answer 1

Step by step explanation

1) 6x-22=2x+34 both the angles are equal to each other because when you biset an angle you break it up into 2 equal parts

2) 4x=56 Collect like integers

3) x=14 Divide both sides by 4 to get x by itself

The answer is x=14

Answer 2

x = 14

`\angle{LMN} = 124\textdegree`

Explanation:

We are given the following information in the question:

We are given an angle LMN. It is bisected by bisector MO.

An angle bisector divides the angle into two equal angles.

`\angle{LMO} = 6x -22\\\angle{MNO} = 2x + 34`

Now, these two angles are equal. Thus, equating them we get:

`6x -22 = 2x + 34\\6x - 2x =34 + 22\\4x = 56\\x =14`

Thus, x = 14.

`\angle{LMN} = 6x -22 + 2x + 34 = 8x + 12 \\\text{Putting x = 14}\\\angle{LMN} = (8* 14) + 12 = 124\textdegree`