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
29°29 degrees
6°6 degrees
53°
53 degrees
To find the measure of each angle, set the two expressions equal to each other:
m∠2 = m∠4
5x+23 = 3x+35
Solve for x:
2x = 12
x = 6
Now substitute the value of x into each expression to find the measures of the angles:
m∠2 = 5(6)+23 = 53 degrees
m∠4 = 3(6)+35 = 53 degrees
Therefore, each angle measures 53 degrees.
wrongg
I apologize for the mistake. Let's solve it correctly:
m∠2 = 5x + 23
m∠4 = 3x + 35
Since vertical angles are congruent, we set the two expressions equal to each other:
5x + 23 = 3x + 35
Subtract 3x from both sides:
5x - 3x + 23 = 35
Combine like terms:
2x + 23 = 35
Subtract 23 from both sides:
2x = 12
Divide both sides by 2:
x = 6
Now substitute the value of x into each expression to find the measures of the angles:
m∠2 = 5(6) + 23 = 30 + 23 = 53 degrees
m∠4 = 3(6) + 35 = 18 + 35 = 53 degrees
Therefore, each angle measures 53 degrees. I apologize for the previous incorrect response.