Answer:
[tex] { \boxed{ \bold{ \tt{ \: m \: = \: 60 \degree \:, n \: = \: 24 \degree}}}}[/tex]
Last option is correct.
Step-by-step explanation:
[tex]{ \text{First, \: let's \: know \: about \: corresponding \: angles}}: [/tex]
Corresponding Angles :
A pair of interior and exterior angles which lies to the same side of the transversal is called corresponding angles. The lines make an F - shape. In our case , 2m° and ( 4m - 120) ° are corresponding angles. Also, Remember that corresponding angles are always equal. Now, Let's create an equation and solve for m.
[tex] \rm \: { \: 2m = 4m - 120}[/tex]
⇢[tex] \rm{2m - 4m \: = - 120}[/tex] { Move 4m to left hand side and change it's sign}
⇢[tex] \rm{ - 2m = - 120}[/tex] { Subtract 4m from 2m}
⇢[tex] \rm{ \frac{ - 2m}{ - 2} = \frac{ - 120}{ - 2}} [/tex] { Divide both sides by -2}
⇢[tex] \rm{ m = 60 \degree}[/tex]
[tex] \text{Now, \: Let's \: know \: about \: vertically \: opposite \: angles} : [/tex]
Vertically opposite angles :
When two lines intersect, the angles formed opposite to each other are called vertically opposite angles. In our case, ( 4m - 120 )° and 5n° are vertically opposite angles. Vertically opposite angles are always equal. Now, Let's create an equation and solve for m.
We have , m = 60°
[tex] \rm{5n = 4m - 120}[/tex]
⇢[tex] \rm{5n \: = \: 4 \times 60 \: - 120}[/tex] { Plug the value of m}
⇢[tex] \rm{5n = 240 - 120}[/tex] { Multiply the numbers : 4 by 60 }
⇢[tex] \rm{5n = 120}[/tex] { Subtract 120 from 240 }
⇢[tex] \rm{ \frac{5n}{5} = \frac{120}{5} }[/tex] { Divide both sides by 5 }
⇢[tex] \rm{n = 24 \degree}[/tex]
[tex] \text{Hope \: I \: helped}[/tex]!
[tex] \text{Best \: regards}[/tex] !
~[tex] \text{TheAnimeGirl}[/tex]
