Two intersecting lines create four angles; ∠2 and ∠4 are a vertical pair. Their sum of their measures is equal to 110° . What equation will solve for the value of each angle?

Answer 1

Let's call ∠2 "x" and ∠4 "y". Since ∠2 and ∠4 are a vertical pair, they are congruent, meaning they have the same measure.

We know that the sum of their measures is equal to 110°, so we can create the equation:

x + y = 110

Since ∠2 and ∠4 are congruent, we can also say that:

x = y

Now we can substitute x for y in the first equation:

x + x = 110

This simplifies to:

2x = 110

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

x = 55

Since x and y are congruent, we can also say that y = 55.

Therefore, the measure of ∠2 and ∠4 is 55° each.

Answer 2

?x = ?
fill in the ?

Answer 3

x = 55

Answer 4

wrong

Answer 5

Apologies for the mistake. Let's revise the solution.

Let's call ∠2 "x" and ∠4 "y". Since ∠2 and ∠4 are a vertical pair, they are congruent, meaning they have the same measure.

We know that the sum of their measures is equal to 110°, so we can create the equation:

x + y = 110

Since ∠2 and ∠4 are congruent, we can also say that:

x = y

Now we can substitute x for y in the first equation:

x + x = 110

This simplifies to:

2x = 110

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

x = 55

Since x and y are congruent, we can also say that y = 55.

Therefore, the measure of ∠2 and ∠4 is 55° each.