Question
For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)
Answers
GPT 3.5
Since vertical angles are opposite each other, they are congruent. Therefore, m∠2 = m∠4.
Setting the two expressions equal to each other:
5x + 23 = 3x + 35
Subtracting 3x from both sides:
5x - 3x + 23 = 35
2x + 23 = 35
Subtracting 23 from both sides:
2x + 23 - 23 = 35 - 23
2x = 12
Dividing both sides by 2:
2x/2 = 12/2
x = 6
Substituting x = 6 into either equation to find the measure of the angles:
m∠2 = 5(6) + 23 = 30 + 23 = 53°
m∠4 = 3(6) + 35 = 18 + 35 = 53°
Therefore, the measure of each angle is 53°.
Setting the two expressions equal to each other:
5x + 23 = 3x + 35
Subtracting 3x from both sides:
5x - 3x + 23 = 35
2x + 23 = 35
Subtracting 23 from both sides:
2x + 23 - 23 = 35 - 23
2x = 12
Dividing both sides by 2:
2x/2 = 12/2
x = 6
Substituting x = 6 into either equation to find the measure of the angles:
m∠2 = 5(6) + 23 = 30 + 23 = 53°
m∠4 = 3(6) + 35 = 18 + 35 = 53°
Therefore, the measure of each angle is 53°.