Question

look at the diagram. which equation can be used to solve for x? 3x + 96 = 111 3x + 6 = 111 3x + 96 = 180 3x + 90 = 180 solve for x. x =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. The angle $(3x + 6)^{\circ}$ and the non - right part of the $111^{\circ}$ angle are vertical angles.
The non - right part of the $111^{\circ}$ angle is $111^{\circ}-90^{\circ}=21^{\circ}$. So, $3x + 6=111 - 90$ which simplifies to $3x+6 = 21$ is wrong. The correct way is to note that the angle adjacent to $(3x + 6)^{\circ}$ and the $111^{\circ}$ angle are vertical angles. The angle adjacent to $(3x + 6)^{\circ}$ is $180-(3x + 6)=174 - 3x$. Since vertical angles are equal, we know that $174-3x=111$. Rearranging gives $3x+111 = 174$ or $3x+96=111$ (because the right - angle part is $90^{\circ}$ and $174-90 = 84$ and $111-90=21$ and $3x+6 + 90=111$).

Step2: Solve the equation for x

Given the equation $3x+96 = 111$.
Subtract 96 from both sides: $3x=111 - 96$.
$3x=15$.
Divide both sides by 3: $x=\frac{15}{3}=5$.

Answer:

A. $3x + 96 = 111$
$x = 5$