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
29°
15.3°
53°
To find the measure of each angle, we need to set the two angles equal to each other and solve for x.
m∠2 = m∠4
5x + 23 = 3x + 35
Subtract 3x from both sides:
2x + 23 = 35
Subtract 23 from both sides:
2x = 12
Divide both sides by 2:
x = 6
Now we can substitute x = 6 back into the expressions for each angle to find their measures.
m∠2 = 5(6) + 23
m∠2 = 30 + 23
m∠2 = 53°
m∠4 = 3(6) + 35
m∠4 = 18 + 35
m∠4 = 53°
Therefore, the measure of each angle is 53°.