Question

given ( mangle orp = 80^{circ} )( mangle orn=(3x + 10)^{circ} )prove ( x = 30 )which statement could be used in step 2 when proving ( x = 30 )?( angle orp ) and ( angle orn ) are a linear pair( angle orp ) and ( angle orn ) are vertical angles( 80 = 3x+10 )( x = 30 )

Explanation:

Step1: Recall linear pair property

A linear pair of angles is supplementary, i.e., their sum is $180^{\circ}$.

Step2: Analyze vertical angles

Vertical angles are equal. But here, $\angle ORP$ and $\angle ORN$ are not vertical angles (vertical angles are opposite angles formed by two intersecting lines).

Step3: Check equation $80 = 3x+10$

This is an equation to solve for $x$, but it is not a statement about the relationship between the angles (which is what step 2 requires). And $x = 30$ is the conclusion (step 5 likely), not step 2.
Since $\angle ORP$ and $\angle ORN$ form a linear - pair (they are adjacent angles and their non - common sides form a straight line), this is the correct statement for step 2.

Answer:

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