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.
1 answer