Question

look at the diagram. which equation can be used to solve for x? 2(x + 5) = 78; 10x = 78; 2(x + 10) = 78; 2x + 5 = 78. solve for x. x =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. The two angles \((x + 5)^{\circ}\) are vertical angles to the non - labeled angles adjacent to the \(78^{\circ}\) angle. The sum of the two \((x + 5)^{\circ}\) angles is equal to the \(78^{\circ}\) angle. So the equation is \(2(x + 5)=78\).

Step2: Solve the equation for \(x\)

First, distribute the 2 on the left - hand side: \(2x+10 = 78\). Then subtract 10 from both sides: \(2x=78 - 10\), so \(2x = 68\). Divide both sides by 2: \(x=\frac{68}{2}=34\).

Answer:

The equation is \(2(x + 5)=78\) and \(x = 34\)