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.
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