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Find the values of my and n ​

Find the values of my and n ​-example-1
User Lmount
by
8.5k points

2 Answers

1 vote

Answer:


{ \boxed{ \bold{ \tt{ \: m \: = \: 60 \degree \:, n \: = \: 24 \degree}}}}

Last option is correct.

Explanation:


{ \text{First, \: let's \: know \: about \: corresponding \: angles}}:

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.


\rm \: { \: 2m = 4m - 120}


\rm{2m - 4m \: = - 120} { Move 4m to left hand side and change it's sign}


\rm{ - 2m = - 120} { Subtract 4m from 2m}


\rm{ ( - 2m)/( - 2) = ( - 120)/( - 2)} { Divide both sides by -2}


\rm{ m = 60 \degree}


\text{Now, \: Let's \: know \: about \: vertically \: opposite \: angles} :

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°


\rm{5n = 4m - 120}


\rm{5n \: = \: 4 * 60 \: - 120} { Plug the value of m}


\rm{5n = 240 - 120} { Multiply the numbers : 4 by 60 }


\rm{5n = 120} { Subtract 120 from 240 }


\rm{ (5n)/(5) = (120)/(5) } { Divide both sides by 5 }


\rm{n = 24 \degree}


\text{Hope \: I \: helped}!


\text{Best \: regards} !

~
\text{TheAnimeGirl}

User Jmromer
by
7.5k points
4 votes

Answer:

m=60 and n=24

Explanation:

Corresponding Angles:

2m = 4m - 120

-2m = -120

m = 60

Vertical Angles:

4m - 120 = 5n

4(60) - 120 = 5n

240 - 120 = 5n

120 = 5n

5n = 120

n = 24

(This is what I got, I apologize if I'm incorrect)

User SomeKittens
by
8.1k points

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