Answer:
[tex]x=11\\j=54\\k=54\\m=126[/tex]
Step-by-step explanation:
The two angles [tex](11x+5)[/tex] and [tex](5x-1)[/tex] are supplementary angles, meaning that their degrees add up to 180°. To find the value of [tex]x[/tex], we can use the following equation:
[tex](11x+5)+(5x-1)= 180[/tex]
Solve for [tex]x[/tex].
[tex](11x+5)+(5x-1)= 180[/tex]
[tex](16x+4)=180[/tex]
[tex]16x=176[/tex]
[tex]x=11[/tex]
After finding the value of [tex]x[/tex], plug the values into the equations.
[tex]11x+5=[/tex]
[tex]11(11)+5=[/tex]
[tex]121+5=126[/tex]
[tex]5x-1=[/tex]
[tex]5(11)-1=[/tex]
[tex]55-1=54[/tex]
Check to make sure your angles add up to 180.
[tex]126+54=180[/tex]
To figure out the rest of our angles, we must look at the given figures. Our 54° angle ([tex]5x-1[/tex]) and [tex]j[/tex] are vertical angles. Vertical angles are congruent which means [tex]j=54[/tex]. Our 126° angle ([tex]11x+5[/tex]) and [tex]m[/tex] are also vertical angles which means [tex]m=126[/tex]. Angle [tex]j[/tex] and angle [tex]k[/tex] are alternate interior angles. Alternate interior angles are also congruent which means [tex]k=54[/tex].
[tex]j=54\\k=54\\m=126[/tex]
~Hope this helps!~
