Two intersecting lines create four angles; ∠1 and ∠3 are a vertical pair. Their sum of their measures is equal to 68°. What equation solves for the value of each angle?

Question

Responses
2x°+68°=180°
x°=68°
2x°=68°
68x°=2°

Answer 1

To find the equations that solve for the measures of the angles ∠1 and ∠3, we can set up the following:

Since ∠1 and ∠3 are vertical angles, they are equal. Let's denote the measure of ∠1 as \( x \) and the measure of ∠3 also as \( x \). According to the problem, their sum is given as:

\[ x + x = 68° \]

This simplifies to:

\[ 2x = 68° \]

So the correct equation to solve for the value of each angle is:

2x° = 68°.