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
53°
53 degrees
15.3°15.3 degrees
29°29 degrees
6°
To find the measure of each angle, we can set the two expressions for the angle measures equal to each other and solve for x.
m∠2 = m∠4
(5x + 23)° = (3x + 35)°
Now, we can solve for x by combining like terms and then isolating x:
5x + 23 = 3x + 35
2x = 12
x = 6
Now that we have the value of x, we can substitute it back into either expression to find the measure of the angles. Let's use m∠2:
m∠2 = (5x + 23)°
m∠2 = (5(6) + 23)°
m∠2 = 53°
Therefore, the measure of angle ∠2 is 53°. The measure of angle ∠4 can be found in the same way:
m∠4 = (3x + 35)°
m∠4 = (3(6) + 35)°
m∠4 = 53°
Therefore, the measure of angle ∠4 is also 53°.