Question

Which statement could be used in step 2 when proving x = 30?

Answer 1

we know that

m∠ORP+m∠ORN=$180\°$ ------> by supplementary angles

substitute the values

$80\°+(3x+10)\°=180\°$

$3x+10=180-80\\ 3x=100-10\\x =90/3\\x =30\°$

therefore

the answer is

$x =30\°$

Answer 2

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.

$\text{ Given}: m\angle ORP=80^o$

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: $\angle ORP\text{ and }\angle ORN$ 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:

$m\angle ORP+m\angle ORN=180$

$80+3x+10=180$

$90+3x=180$

$90-90+3x=180-90$

$3x=90$

$\frac{3x}{3}=\frac{90}{3}$

$x=30$

Hence proved.