Question

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

Given: m< ORP = 80
m Prove: x = 30

Answer options :
A.) B.) C.) 80= 3x + 10
D.) c=30

Answer 1

Option A is the correct choice.

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`

`(3x)/(3)=(90)/(3)`

`x=30`

Hence proved.