Question

given: $m\angle orp = 80^\circ$
$m\angle orn = (3x + 10)^\circ$
prove: $x = 30$
which statement could be used in step 2 when proving $x = 30$

statements	reasons
2.	2.
3.	3.
4.	4.
5.	5.

$\bigcirc$ $\angle orp$ and $\angle orn$ are a linear pair
$\bigcirc$ $\angle orp$ and $\angle orn$ are vertical angles
$\bigcirc$ $80 = 3x +10$
$\bigcirc$ $x = 30$

Explanation:

Step1: Identify angle relationship

From the diagram, $\angle ORP$ and $\angle ORN$ form a straight line at point $R$, so they are a linear pair. Linear pairs are supplementary, meaning their measures add to $180^\circ$, but first we state their relationship.

Step2: Evaluate option validity

• $\angle ORP$ and $\angle ORN$ are vertical angles: Incorrect, vertical angles are opposite each other, not adjacent on a line.
• $80 = 3x +10$: This is a later step using the linear pair property, not step 2.
• $x = 30$: This is the final conclusion, not step 2.
• $\angle ORP$ and $\angle ORN$ are a linear pair: Correct, this is the foundational relationship to start the proof after given statements.

Answer:

$\boldsymbol{\angle ORP \text{ and } \angle ORN \text{ are a linear pair}}$