To solve for the measures of the angles ∠2 and ∠4, we can use the information that they are vertical angles. Vertical angles are equal to each other.
Let's denote the measure of ∠2 as \( x \) and since ∠4 is a vertical angle, its measure can also be denoted as \( x \).
According to the problem, the sum of their measures is equal to 110°. Therefore, we can write the equation as:
\[ x + x = 110° \]
This simplifies to:
\[ 2x = 110° \]
To solve for \( x \), we can divide both sides by 2:
\[ x = 55° \]
Thus, each angle measures 55°.
The final equation that can solve for the value of each angle is:
\[ x° + x° = 110° \]
or
\[ 2x° = 110° \]
Therefore, filling in the blanks you provided would result in:
x° = 55°.
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