Question
Two intersecting lines create four angles. <1 and <3 are a vertical pair. Their sum of their measures is equal to 68 degrees. What equation solves for the value of each angle.
Answers
Answered by
GPT 3.5
Let's call the measures of angles <1 and <3 as x and y, respectively.
We know that <1 and <3 are a vertical pair, which means they are congruent. Therefore, x = y.
We are also given that the sum of their measures is equal to 68 degrees. So, x + y = 68.
Since x = y, we can substitute x in the equation above with y.
Therefore, y + y = 68.
Simplifying, we have 2y = 68.
Now, let's solve for y by dividing both sides of the equation by 2.
2y/2 = 68/2
y = 34
Since x = y, we have x = 34.
Therefore, the measure of angle <1 is 34 degrees and the measure of angle <3 is also 34 degrees.
We know that <1 and <3 are a vertical pair, which means they are congruent. Therefore, x = y.
We are also given that the sum of their measures is equal to 68 degrees. So, x + y = 68.
Since x = y, we can substitute x in the equation above with y.
Therefore, y + y = 68.
Simplifying, we have 2y = 68.
Now, let's solve for y by dividing both sides of the equation by 2.
2y/2 = 68/2
y = 34
Since x = y, we have x = 34.
Therefore, the measure of angle <1 is 34 degrees and the measure of angle <3 is also 34 degrees.
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