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?(1 point)

Question

__x = __

Answer 1

∠2 and ∠4 are a vertical pair, which means they are opposite angles formed by the intersection of the lines. Therefore, they are congruent.

Thus, let's assume the measure of each angle is x.

The equation to solve for x is:
x + x = 110

Simplifying the equation:
2x = 110

Dividing both sides by 2:
x = 55

Therefore, the value of each angle is:
x = 55

So, the equation to solve for the value of each angle is:
x = 55.

Answer 2

wrong

Answer 3

Apologies for the incorrect response. Let me provide the correct solution.

Let's assume ∠2 and ∠4 have measures x and y, respectively.

According to the given information, the sum of the measures of ∠2 and ∠4 is equal to 110°:

x + y = 110

Since ∠2 and ∠4 are a vertical pair, they are congruent:

x = y

Now we have a system of equations:

x + y = 110
x = y

To solve this system, we can substitute the value of x from the second equation into the first equation:

x + x = 110

Combining like terms:

2x = 110

Dividing both sides by 2:

x = 55

Now we can substitute the value of x back into one of the equations to find the value of y. Let's use the second equation:

y = x = 55

Therefore, the value of each angle is:

x = 55
y = 55

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

x = 55
y = 55