Question
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?
Answers
GPT 3.5
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.
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.