Two intersecting lines create four angles 1 and three vertical pair there's some other measures is equal to 68 1 equation solves the value of each angle?

Answer 1

Let's call the four angles created by the intersecting lines Angle 1, Angle 2, Angle 3, and Angle 4.

Given that Angle 1 and Angle 3 are vertical angles, they are congruent and have equal measures.

Similarly, Angle 2 and Angle 4 are also vertical angles, so they are congruent and have equal measures.

Therefore, we have two sets of congruent angles: Angle 1 = Angle 3 and Angle 2 = Angle 4.

Since Angle 1 and Angle 3 together have a sum of 68 degrees according to the problem, we can set up the following equation:
Angle 1 + Angle 3 = 68.

By substituting Angle 1 = Angle 3 into the equation, we get:
2 x Angle 1 = 68.

Dividing both sides of the equation by 2, we find:
Angle 1 = 68 / 2 = 34.

Now we know that Angle 1 has a measure of 34 degrees. Since Angle 3 is congruent to Angle 1, Angle 3 also has a measure of 34 degrees.

Similarly, since Angle 2 and Angle 4 are congruent, and Angle 2 is vertical to Angle 1, we know that it also has a measure of 34 degrees.

In conclusion, each of the angles, Angle 1, Angle 2, Angle 3, and Angle 4, has a measure of 34 degrees.