Question

look at the diagram.
which equation can be used to solve for x?
10x = 78
2(x + 5) = 78
2x + 5 = 78
2(x + 10) = 78
solve for x.
x =
submit
work it out
need help? these can help:

Explanation:

Step1: Analyze vertical angles

Vertical angles are equal. The two angles \((x + 5)^{\circ}\) are vertical angles. The sum of the two \((x + 5)^{\circ}\) angles and \(78^{\circ}\) forms a linear pair. But since the two \((x + 5)^{\circ}\) angles are adjacent to \(78^{\circ}\) and form a linear pair, we know that \(2(x + 5)=78\) (because the sum of adjacent angles forming a linear pair is \(180^{\circ}\), but here we have two equal angles \((x + 5)\) and \(78^{\circ}\) where \(2(x + 5)+78 = 180\) is wrong. Wait, no, actually, if we consider the property of angles around a point. Wait, no, looking at the diagram, the two \((x + 5)\) angles and \(78^{\circ}\) are related as \(2(x + 5)=78\) (because of the angle - relationship in the diagram, assume they are vertical - adjacent in a way that the two \((x + 5)\) angles are equal and their sum is equal to the non - adjacent angle \(78^{\circ}\) in terms of the equation setup for solving \(x\)).

Step2: Solve the equation \(2(x + 5)=78\)

First, use the distributive property: \(2x+10 = 78\). 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 \(2(x + 5)=78\) is used to solve for \(x\), and \(x = 34\).