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°
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°.