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 6°6 degrees 53° 53 degrees
To find the measures of each angle, we need to set the two vertical angles equal to each other because vertical angles are congruent.
So, we have:
5x + 23 = 3x + 35
Subtract 3x from both sides to isolate x:
2x + 23 = 35
Subtract 23 from both sides to isolate x:
2x = 12
Divide by 2 to solve for x:
x = 6
Now, substitute x back into one of the expressions to find the measure of each angle:
m∠2 = 5(6) + 23 = 30 + 23 = 53°
m∠4 = 3(6) + 35 = 18 + 35 = 53°
Therefore, the measure of each angle is 53 degrees.