Question

Two intersecting lines create four angles; ∠1 and ∠3 are a vertical pair. The sum of their measures is equal to 68° . Which two equations would solve for the value of each angle?(2 points)
Responses

x=68°x is equal to 68 degrees

x+x=68x plus x is equal to 68

2x=682 x is equal to 68

2x+68=180

Answer 1

To solve for the measures of angles ∠1 and ∠3, which are vertical angles, you can use the fact that vertical angles are equal to each other. Therefore, if we let the measure of each angle be represented by \( x \), we have:

1. \( x = x \) (since vertical angles are equal)
2. The problem states that the sum of ∠1 and ∠3 is equal to 68°, which translates to the equation:
\[
x + x = 68°
\]
or
\[
2x = 68°
\]

So the two equations that would solve for the value of each angle are:

1. \( 2x = 68° \)
2. \( x + x = 68° \)

These equations can be simplified to find the value of \( x \), which represents the measures of angles ∠1 and ∠3.