For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)°, what is the measure of each angle?(1 point) Responses 29°29 degrees 53° 53 degrees 15.3°15.3 degrees 6°6 degrees
To find the measure of each angle, we set the two expressions for the angles equal to each other:
m∠2 = m∠4
(5x + 23)° = (3x + 35)°
Simplifying the equation, we can subtract (3x + 35)° from both sides:
2x - 12 = 0
Adding 12 to both sides, we have:
2x = 12
Dividing both sides by 2, we get:
x = 6
Now we can substitute the value of x back into one of the expressions to find the measure of each angle:
m∠2 = 5(6) + 23
m∠2 = 53°
m∠4 = 3(6) + 35
m∠4 = 53°
Therefore, the measure of each angle is 53°.