For two vertical angles with measures m∠1 = (4x + 26) ° and m∠3 = (3x + 32) ° , what is the measure of each angle?(1 point) Responses 6° 6degree 24° 24degree 50° 50degree 64°

Answer 1

To find the measure of each angle, we can set up an equation using the fact that vertical angles are congruent:

m∠1 = m∠3

(4x + 26)° = (3x + 32)°

Now let's solve for x:

4x + 26 = 3x + 32

Subtract 3x from both sides:

4x - 3x + 26 = 3x - 3x + 32

x + 26 = 32

Subtract 26 from both sides:

x + 26 - 26 = 32 - 26

x = 6

Now we can substitute x = 6 back into either equation to find the measure of the angles. Let's use the first one:

m∠1 = (4x + 26)°

m∠1 = (4(6) + 26)°

m∠1 = (24 + 26)°

m∠1 = 50°

Therefore, the measure of each angle is 50°.