Question
For two verticle angles with measures m<1=(2x+26) and m<3=(3x+32) what is the measure of each angle?
Answers
GPT 3.5
Vertical angles are formed by two intersecting lines and are always congruent. Therefore, we can set up an equation and solve for x to find the value of each angle.
Since vertical angles are congruent, we have:
m<1 = m<3
(2x + 26) = (3x + 32)
Rearranging to isolate terms with x:
2x - 3x = 32 - 26
-x = 6
Dividing both sides by -1 to solve for x:
x = -6
Now we can substitute x back into either m<1 or m<3 to find the measure of each angle. Let's use m<1:
m<1 = 2x + 26 = 2(-6) + 26 = -12 + 26 = 14
Therefore, the measure of angle 1 (<1) is 14 degrees.
Since vertical angles are congruent, the measure of angle 3 (<3) is also 14 degrees.
Since vertical angles are congruent, we have:
m<1 = m<3
(2x + 26) = (3x + 32)
Rearranging to isolate terms with x:
2x - 3x = 32 - 26
-x = 6
Dividing both sides by -1 to solve for x:
x = -6
Now we can substitute x back into either m<1 or m<3 to find the measure of each angle. Let's use m<1:
m<1 = 2x + 26 = 2(-6) + 26 = -12 + 26 = 14
Therefore, the measure of angle 1 (<1) is 14 degrees.
Since vertical angles are congruent, the measure of angle 3 (<3) is also 14 degrees.