Question

look at the diagram. which equation can be used to solve for x? 3x + 96 = 111, 3x + 96 = 180, 3x + 6 = 111, 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 - labeled angle adjacent to the \(111^{\circ}\) angle are vertical angles. The non - labeled angle adjacent to the \(111^{\circ}\) angle and the \(111^{\circ}\) angle form a linear pair, so the non - labeled angle is \(180 - 111=69^{\circ}\). Also, we know that the sum of the angle \((3x + 6)^{\circ}\) and the \(90^{\circ}\) angle and the non - labeled angle is \(180^{\circ}\). The non - labeled angle is \(180-(90+(3x + 6))\). Since vertical angles are equal, we can also note that the sum of the \(90^{\circ}\) angle, the \((3x + 6)^{\circ}\) angle and the angle that is vertical to the part of the \(180^{\circ}\) around point \(B\) gives us the equation. The correct way is to consider the fact that the sum of the \(90^{\circ}\) angle, the \((3x + 6)^{\circ}\) angle and the angle adjacent to the \(111^{\circ}\) angle (which is \(180 - 111 = 69^{\circ}\)) is \(180^{\circ}\). So \(3x+6 + 90=180-(180 - 111)\), simplified, we get \(3x+96 = 111\).

Step2: Solve the equation for \(x\)

First, subtract 96 from both sides of the equation \(3x+96 = 111\).
\(3x=111 - 96\)
\(3x = 15\)
Then divide both sides by 3: \(x=\frac{15}{3}=5\)

Answer:

The equation is \(3x + 96 = 111\), \(x = 5\)