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 6° 6 degrees 53° 53 degrees
To find the measure of each angle, we need to set up an equation.
By the vertical angle theorem, vertical angles are congruent, meaning they have the same measure.
So, we can set up the equation:
5x + 23 = 3x + 35
To solve for x, we subtract 3x from both sides of the equation:
5x - 3x + 23 = 3x - 3x + 35
2x + 23 = 35
Next, we subtract 23 from both sides:
2x + 23 - 23 = 35 - 23
2x = 12
Finally, we divide both sides by 2 to solve for x:
2x/2 = 12/2
x = 6
Now that we have the value of x, we can substitute it back into the equations for the measures of the angles:
m∠2 = 5x + 23
m∠2 = 5(6) + 23
m∠2 = 30 + 23
m∠2 = 53°
m∠4 = 3x + 35
m∠4 = 3(6) + 35
m∠4 = 18 + 35
m∠4 = 53°
So, the measure of each angle is 53°.