Question
Two angles make a vertical pair: m<1 = (3x + 15) ° and m/3 = (x + 45)°. What is the measure of each angle?
Answers
GPT 3.5
Since the two angles are a vertical pair, they are equal in measure. Therefore, we can set their expressions equal to each other:
3x + 15 = x + 45
Subtract x from both sides:
2x + 15 = 45
Subtract 15 from both sides:
2x = 30
Divide both sides by 2:
x = 15
Now, we can find the measure of each angle by substituting x back into the expressions:
m<1 = 3(15) + 15 = 45 + 15 = 60°
m<3 = 15 + 45 = 60°
So, each angle measures 60°.
3x + 15 = x + 45
Subtract x from both sides:
2x + 15 = 45
Subtract 15 from both sides:
2x = 30
Divide both sides by 2:
x = 15
Now, we can find the measure of each angle by substituting x back into the expressions:
m<1 = 3(15) + 15 = 45 + 15 = 60°
m<3 = 15 + 45 = 60°
So, each angle measures 60°.