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 15.3°15.3 degrees 53° 53 degrees 6°6 degrees
To find the measure of each angle, we need to set the expressions for each angle equal to each other and solve for x.
Setting the expressions equal to each other:
(5x+23)° = (3x+35)°
Now we can solve for x.
5x+23 = 3x+35
Subtracting 3x from both sides:
2x+23 = 35
Subtracting 23 from both sides:
2x = 12
Dividing both sides by 2:
x = 6
Now that we have the value of x, we can substitute it back into one of the expressions to find the measure of the angles.
m∠2 = (5x+23)°
m∠2 = (5*6 + 23)°
m∠2 = (30 + 23)°
m∠2 = 53°
m∠4 = (3x+35)°
m∠4 = (3*6 + 35)°
m∠4 = (18 + 35)°
m∠4 = 53°
Therefore, the measure of each angle is 53 degrees.