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

what do you mean by "each angle"? Just the vertical pair, or each of the four angles?

It is true that ∠1 + ∠3 = 68° but since vertical angles are congruent, that means that
∠1 + ∠1 = 68°
so ∠1 = ∠3 = 34°
and so ∠2 = ∠4 = 146°

The correct answer is 2x = 68.

oi!

To solve for the value of each angle, we can assign variables to the unknown angles and use the given information to set up an equation.

Let's say ∠1 has a measure of x degrees. Since ∠1 and ∠3 are a vertical pair, ∠3 will also have a measure of x degrees.

According to the given information, the sum of ∠1 and ∠3 is equal to 68°. Therefore, we can set up the following equation:

∠1 + ∠3 = 68

Substituting the values for ∠1 and ∠3:

x + x = 68

Combining like terms:

2x = 68

To solve for x, we divide both sides of the equation by 2:

2x/2 = 68/2

x = 34

Therefore, ∠1 has a measure of 34° and ∠3 also has a measure of 34°.