Question
For two vertical angles with measures m<1 = (2x + 26) ° and m<3 = (3x + 32)", what is the measure of each angle? (1 point)
Answers
GPT 3.5
To find the measure of each angle, we set the measures of the two vertical angles equal to each other:
2x + 26 = 3x + 32
Subtracting 2x from both sides gives:
26 = x + 32
Subtracting 32 from both sides gives:
-6 = x
Now that we have found the value of x, we can substitute it back into either of the original angle measures to find the measure of each angle. Let's substitute it into the measure of angle 1:
m<1 = 2x + 26
m<1 = 2(-6) + 26
m<1 = -12 + 26
m<1 = 14
Therefore, the measure of angle 1 is 14°.
Now, we can find the measure of angle 3 by substituting x back into its measure:
m<3 = 3x + 32
m<3 = 3(-6) + 32
m<3 = -18 + 32
m<3 = 14
Therefore, the measure of angle 3 is also 14°.
2x + 26 = 3x + 32
Subtracting 2x from both sides gives:
26 = x + 32
Subtracting 32 from both sides gives:
-6 = x
Now that we have found the value of x, we can substitute it back into either of the original angle measures to find the measure of each angle. Let's substitute it into the measure of angle 1:
m<1 = 2x + 26
m<1 = 2(-6) + 26
m<1 = -12 + 26
m<1 = 14
Therefore, the measure of angle 1 is 14°.
Now, we can find the measure of angle 3 by substituting x back into its measure:
m<3 = 3x + 32
m<3 = 3(-6) + 32
m<3 = -18 + 32
m<3 = 14
Therefore, the measure of angle 3 is also 14°.