Question

Two interesting 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

Since angles \( \angle 2 \) and \( \angle 4 \) are a vertical pair, they are equal in measure. Let's denote the measure of each angle as \( x \).

According to the problem, the sum of the measures of \( \angle 2 \) and \( \angle 4 \) is equal to 110 degrees. Therefore, we can write the equation as:

\[
x + x = 110
\]

This simplifies to:

\[
2x = 110
\]

To find the value of \( x \), divide both sides by 2:

\[
x = \frac{110}{2}
\]

\[
x = 55
\]

Therefore, each angle \( \angle 2 \) and \( \angle 4 \) measures 55 degrees. The equation to solve for the value of each angle is:

\[
2x = 110
\]