Respuesta :

calculista

we know that

m∠ORP+m∠ORN=[tex]180\°[/tex] ------> by supplementary angles

substitute the values

[tex]80\°+(3x+10)\°=180\°[/tex]

[tex]3x+10=180-80\\ 3x=100-10\\x =90/3\\x =30\°[/tex]

therefore

the answer is

[tex]x =30\°[/tex]

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given a graph of angles formed around a line and we are asked to choose the correct option that could be used in step 2 to prove that x equals 30.

[tex]\text{ Given}: m\angle ORP=80^o[/tex]

We can see that angle ORP and angle ORN (3x+10) forms a linear pair as they are adjacent and formed by line PN intersected by line MO.

Therefore, the step 2 to prove that measure of x is 30 will be: [tex]\angle ORP\text{ and }\angle ORN[/tex] is linear pair of angles and option A is the correct choice.

Let us solve for x.

Since linear pair of angles add up-to 180 degrees, so we can set an equation as:

[tex]m\angle ORP+m\angle ORN=180[/tex]

[tex]80+3x+10=180[/tex]

[tex]90+3x=180[/tex]

[tex]90-90+3x=180-90[/tex]

[tex]3x=90[/tex]

[tex]\frac{3x}{3}=\frac{90}{3}[/tex]

[tex]x=30[/tex]

Hence proved.

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