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
15.3°15.3 degrees
53°
53 degrees
6°6 degrees
29°
To find the measure of each angle, we set the measures of the vertical angles equal to each other since vertical angles are congruent.
5x + 23 = 3x + 35
Subtract 3x from both sides:
2x + 23 = 35
Subtract 23 from both sides:
2x = 12
Divide by 2:
x = 6
Now, we can substitute x = 6 into either equation to find the measure of the angles:
m∠2 = 5(6) + 23 = 53 degrees
m∠4 = 3(6) + 35 = 53 degrees
Therefore, the measure of each angle is 53 degrees.