Two intersecting lines, create four angles, two and four are a vertical pair there some of their measure is equal to 110. What equation will solve for the value of each angle.
Let's call the four angles formed by the intersecting lines as angle 1, angle 2, angle 3, and angle 4.
We are given that angles 2 and 4 are a vertical pair, which means they are congruent. Therefore, we can say:
angle 2 = angle 4
We are also given that the sum of their measures is equal to 110. Therefore, we can write the equation:
angle 2 + angle 4 = 110
Since angle 2 is equal to angle 4, we can substitute angle 2 with angle 4:
angle 4 + angle 4 = 110
2 * angle 4 = 110
Now, we can solve for the measure of angle 4 by dividing both sides by 2:
angle 4 = 110 / 2
angle 4 = 55
Since angle 2 and angle 4 are congruent, angle 2 must also be equal to 55.
Therefore, the value of each angle is 55 degrees.