Question

What is X , J , K , and M

Answer 1

`x=11\\j=54\\k=54\\m=126`

Explanation:

The two angles
`(11x+5)` and
`(5x-1)` are supplementary angles, meaning that their degrees add up to 180°. To find the value of
`x`, we can use the following equation:

`(11x+5)+(5x-1)= 180`

Solve for
`x`.

`(11x+5)+(5x-1)= 180`

`(16x+4)=180`

`16x=176`

`x=11`

After finding the value of
`x`, plug the values into the equations.

`11x+5=`

`11(11)+5=`

`121+5=126`

`5x-1=`

`5(11)-1=`

`55-1=54`

Check to make sure your angles add up to 180.

`126+54=180`

To figure out the rest of our angles, we must look at the given figures. Our 54° angle (
`5x-1`) and
`j` are vertical angles. Vertical angles are congruent which means
`j=54`. Our 126° angle (
`11x+5`) and
`m` are also vertical angles which means
`m=126`. Angle
`j` and angle
`k` are alternate interior angles. Alternate interior angles are also congruent which means
`k=54`.

`j=54\\k=54\\m=126`

~Hope this helps!~