Two intersecting lines create 4 angles; <2 and <4 r a vertical pair. Their sum of their measures is equal to 110. wut equation will solve for the value of each angle?

Question

___x = ___

Answer 1

To solve for the measures of angles <2 and <4, let's denote the measure of angle <2 as $x$ and the measure of angle <4 as $y$.

Since <2 and <4 form a vertical pair, they are equal in measure. Therefore, we have:

$$x=y$$

According to the information given, the sum of their measures is equal to 110 degrees:

$$x+y=110$$

Substituting $y$ with $x$ in the sum equation gives:

$$x+x=110$$

This simplifies to:

$$2x=110$$

Now, you can solve for $x$. To do that, divide both sides by 2:

$$x=55$$

Thus, the measures of both angles <2 and <4 are:

$$x=55\text{ degrees}$$ $$y=55\text{ degrees}$$

The full equation to solve for the value of each angle can be written as:

$$2x=110$$

where $x$ represents the measure of angles <2 and <4.