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
6°6 degrees
29°29 degrees
15.3°15.3 degrees
53°
To find the measure of each angle, we set the two expressions equal to each other and solve for x:
5x + 23 = 3x + 35
Combine like terms:
2x + 23 = 35
Subtract 23 from both sides:
2x = 12
Divide both sides by 2:
x = 6
Now that we have the value of x, we can substitute it into either expression to find the measure of the angles. Let's use the first expression:
m∠2 = 5(6) + 23
m∠2 = 30 + 23
m∠2 = 53°
Therefore, the measure of angle 2 is 53°. To find the measure of angle 4, substitute x = 6 into the second expression:
m∠4 = 3(6) + 35
m∠4 = 18 + 35
m∠4 = 53°
Therefore, the measure of angle 4 is also 53°.