Question

given: m∠orp = 80°
m∠orn=(3x + 10)°
prove: x = 30
which statement could be used in step 2 when proving x = 30?
statements reasons

1. m∠orp = 80°, m∠orn=(3x + 10)° 1. given

2.
3.
4.
5.
∠orp and ∠orn are a linear pair
∠orp and ∠orn are vertical angles
80 = 3x+10
x = 30

Explanation:

Step1: Identify angle - relationship

Since $\angle ORP$ and $\angle ORN$ are adjacent and form a straight - line at point $R$, they are a linear pair. The sum of angles in a linear pair is $180^{\circ}$.

Step2: Set up the equation

If $\angle ORP = 80^{\circ}$ and $\angle ORN=(3x + 10)^{\circ}$, then $80+(3x + 10)=180$. But in the context of the proof steps, the first step after stating the given angles is to state the angle - relationship. So the statement for step 2 is that $\angle ORP$ and $\angle ORN$ are a linear pair.

Answer:

$\angle ORP$ and $\angle ORN$ are a linear pair