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

1. $m\angle orp = 80^{circ};m\angle orn=(3x + 10)^{circ}$ 1. given

2.
3.
4.
5.

1. 3. 4. 5.

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

Explanation:

Step1: Identify angle - relationship

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

Step2: Set up the equation

If $m\angle ORP = 80^{\circ}$ and $m\angle ORN=(3x + 10)^{\circ}$, then $80+(3x + 10)=180$. Simplifying the left - hand side gives $3x+90 = 180$. Subtracting 90 from both sides gives $3x=90$, and dividing both sides by 3 gives $x = 30$. In the proof steps, after stating the given angle measures, the next logical step is to use the linear - pair relationship. So the statement that could be used in step 2 is $\angle ORP$ and $\angle ORN$ are a linear pair.

Answer:

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