Question

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)
x° = °

Answer 1

When two lines intersect, they create pairs of vertical angles that are equal in measure. In this case, ∠2 and ∠4 are vertical angles, which means:

\[
\angle 2 = \angle 4
\]

Given that the sum of their measures is equal to 110°, we can set up the following equation:

\[
\angle 2 + \angle 4 = 110°
\]

Since ∠2 and ∠4 are equal, we can substitute ∠4 with ∠2 in the equation:

\[
\angle 2 + \angle 2 = 110°
\]

This simplifies to:

\[
2\angle 2 = 110°
\]

To find the measure of each angle, we divide both sides by 2:

\[
\angle 2 = \frac{110°}{2} = 55°
\]

Thus, the measures of both ∠2 and ∠4 are 55°.

So, the equation that solves for the value of each angle is:

\[
x° = 55°
\]

Where \( x \) represents either angle.