For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?

Answer 1

Vertical angles are a pair of angles formed when two lines intersect. They are always congruent, meaning they have the same measure. Therefore, m∠2 = m∠4.

Given that m∠2 = (5x+23)° and m∠4 = (3x+35)°, we can set up an equation:

(5x+23)° = (3x+35)°

Now we can solve for x by subtracting 3x from both sides and subtracting 23 from both sides:

5x - 3x = 35 - 23
2x = 12
x = 6

Now we can substitute the value of x back into one of the angle measures to find the measure of each angle:

m∠2 = 5x + 23
m∠2 = 5(6) + 23
m∠2 = 30 + 23
m∠2 = 53°

So, m∠2 = 53° and m∠4 = 53°.