Respuesta :

calculista

we know that

In a parallelogram opposite angles are congruent and consecutive angles are supplementary.

So

m∠O=m∠M

m∠L=m∠N

m∠O+m∠L=[tex] 180 [/tex]

Step [tex] 1 [/tex]

Find the value of x

[tex] (x+20)+(2x+10)=180\\ 3x+30=180\\ 3x=180-30\\ x=\frac{150}{3} \\ \\ x=50\ degrees [/tex]

Step [tex] 2 [/tex]

Find the value of angle L

m∠L[tex] =(2x+10) [/tex]

m∠L[tex] =(2*50+10) [/tex]

m∠L[tex] =110\ degrees [/tex]

Remember that

m∠N=m∠L

m∠N=[tex] 110\ degrees [/tex]

therefore

the answer is

the measure of the angle N is equal to [tex] 110\ degrees [/tex]

The measure of angle N is 110°

How to determine the angle

It is important to note that opposite angles of a parallelogram and consecutive angles are supplementary( 180)°

So,

2x + 10° = ∠N

But we need to find the value of x

From the diagram, we have that (2x + 10)° and (x + 20)° are on a straight line. Angles on  straight line are equal to 180°

2x+ 10 + x + 20 = 180°

Collect like terms

3x + 30 = 180

3x = 180 - 30

3x = 150

x = 150/3

x = 50°

But we have that opposite sides of a parallelogram are equal

So ∠ L (2x + 10)° = ∠N

Substitute the value of x

∠N = 2x + 10

∠N = 2(50) + 10

∠N = 100 + 10

∠N = 110°

Thus, the measure of angle N is 110°

Learn more about a parallelogram here:

https://brainly.com/question/331095

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